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Journal articles on the topic 'Complete congruence'

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Published: 4 June 2021

Last updated: 19 February 2022

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1

FAN, XINGKUI, QIANHUA CHEN, and XIANGJUN KONG. "COMPLETE LATTICE HOMOMORPHISM OF STRONGLY REGULAR CONGRUENCES ON -INVERSIVE SEMIGROUPS." Journal of the Australian Mathematical Society 100, no. 2 (October 28, 2015): 199–215. http://dx.doi.org/10.1017/s1446788715000373.

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In this paper, we investigate strongly regular congruences on $E$-inversive semigroups $S$. We describe the complete lattice homomorphism of strongly regular congruences, which is a generalization of an open problem of Pastijn and Petrich for regular semigroups. An abstract characterization of left and right traces for strongly regular congruences is given. The strongly regular (sr) congruences on $E$-inversive semigroups $S$ are described by means of certain strongly regular congruence triples $({\it\gamma},K,{\it\delta})$ consisting of certain sr-normal equivalences ${\it\gamma}$ and ${\it\delta}$ on $E(S)$ and a certain sr-normal subset $K$ of $S$. Further, we prove that each strongly regular congruence on $E$-inversive semigroups $S$ is uniquely determined by its associated strongly regular congruence triple.

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2

Liang, Xiquan, Li Yan, and Junjie Zhao. "Linear Congruence Relation and Complete Residue Systems." Formalized Mathematics 15, no. 4 (January 1, 2007): 181–87. http://dx.doi.org/10.2478/v10037-007-0022-7.

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Linear Congruence Relation and Complete Residue Systems In this paper, we defined the congruence relation and proved its fundamental properties on the base of some useful theorems. Then we proved the existence of solution and the number of incongruent solution to a linear congruence and the linear congruent equation class, in particular, we proved the Chinese Remainder Theorem. Finally, we defined the complete residue system and proved its fundamental properties.

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3

Gigoń, Roman S. "Completely simple congruences on E-inversive semigroups." Journal of Algebra and Its Applications 15, no. 06 (March 30, 2016): 1650052. http://dx.doi.org/10.1142/s0219498816500523.

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We study completely simple congruences on an arbitrary [Formula: see text]-inversive semigroup [Formula: see text]. In particular, we show that every such congruence [Formula: see text] on [Formula: see text] is uniquely determined by its kernel and trace, and that the trace of [Formula: see text] is a congruence on the biordered set [Formula: see text]. Moreover, we investigate the complete lattice of all completely simple congruences on [Formula: see text] and show that the trace relation is a complete congruence on this lattice. We also construct a family of completely simple congruences on [Formula: see text].

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4

Gratzer, G., and H. Lakser. "On Complete Congruence Lattices of Complete Lattices." Transactions of the American Mathematical Society 327, no. 1 (September 1991): 385. http://dx.doi.org/10.2307/2001848.

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5

Grätzer, G., and H. Lakser. "On complete congruence lattices of complete lattices." Transactions of the American Mathematical Society 327, no. 1 (January 1, 1991): 385–405. http://dx.doi.org/10.1090/s0002-9947-1991-1036003-5.

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6

Gratzer, G., and E. T. Schmidt. "Complete Congruence Lattices of Complete Distributive Lattices." Journal of Algebra 171, no. 1 (January 1995): 204–29. http://dx.doi.org/10.1006/jabr.1995.1009.

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7

FREESE, R., G. GRÄTZE, and E. T. SCHMIDT. "ON COMPLETE CONGRUENCE LATTICES OF COMPLETE MODULAR LATTICES." International Journal of Algebra and Computation 01, no. 02 (June 1991): 147–60. http://dx.doi.org/10.1142/s0218196791000080.

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The lattice of all complete congruence relations of a complete lattice is itself a complete lattice. In 1988, the second author announced the converse: every complete lattice L can be represented as the lattice of complete congruence relations of some complete lattice K. In this paper we improve this result by showing that K can be chosen to be a complete modular lattice.

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8

Kehayopulu, Niovi. "On Semilattice Congruences on Hypersemigroups and on Ordered Hypersemigroups." European Journal of Pure and Applied Mathematics 11, no. 2 (April 27, 2018): 476–92. http://dx.doi.org/10.29020/nybg.ejpam.v11i2.3266.

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We prove that if $H$ is an hypersemigroup (resp. ordered hypersemigroup) and $\sigma$ is a semilattice congruence (resp. complete semilattice congruence) on $H$, then there exists a family $\cal A$ of proper prime ideals of $H$ such that $\sigma$ is the intersection of the semilattice congruences $\sigma_I$, $I\in\cal A$ ($\sigma_I$ is the known relation defined by $a\sigma_I b$ $\Leftrightarrow$ $a,b\in I$ or $a,b\notin I$). Furthermore, we study the relation between the semilattices of an ordered semigroup and the ordered hypersemigroup derived by the hyperoperations $a\circ b=\{ab\}$ and $a\circ b:=\{t\in S \mid t\le ab\}$. We introduce the concept of a pseudocomplete semilattice congruence as a semilattice congruence $\sigma$ for which $\le\subseteq\sigma$ and we prove, among others, that if $(S,\cdot,\le)$ is an ordered semigroup, $(S,\circ,\le)$ the hypersemigroup defined by $t\in a\circ b$ if and only if $t\le ab$ and $\sigma$ is a pseudocomplete semilattice congruence on $(S,\cdot,\le)$, then it is a complete semilattice congruence on $(S,\circ,\le)$. Illustrative examples are given.

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9

AICHINGER, ERHARD, and JÜRGEN ECKER. "EVERY (k + 1)-AFFINE COMPLETE NILPOTENT GROUP OF CLASS k IS AFFINE COMPLETE." International Journal of Algebra and Computation 16, no. 02 (April 2006): 259–74. http://dx.doi.org/10.1142/s0218196706002858.

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We let G be a group, and we let k be a natural number. We assume that G is nilpotent of class at most k, and that every (k + 1)-ary congruence preserving function on G is a polynomial function. We show that then every congruence preserving function on G (of any finite arity) is a polynomial function.

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10

Kaarli, K., and R. McKenzie. "Affine complete varieties are congruence distributive." Algebra Universalis 38, no. 3 (May 1, 1997): 329–54. http://dx.doi.org/10.1007/s000120050058.

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11

Giacobazzi, R., and F. Ranzato. "Some properties of complete congruence lattices." Algebra Universalis 40, no. 2 (December 1, 1998): 189–200. http://dx.doi.org/10.1007/s000120050089.

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12

Katsov, Yefim, Tran Giang Nam, and Jens Zumbrägel. "On simpleness of semirings and complete semirings." Journal of Algebra and Its Applications 13, no. 06 (April 20, 2014): 1450015. http://dx.doi.org/10.1142/s0219498814500157.

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In this paper, we investigate various classes of semirings and complete semirings regarding the property of being ideal-simple, congruence-simple, or both. Among other results, we describe (complete) simple, i.e. simultaneously ideal- and congruence-simple, endomorphism semirings of (complete) idempotent commutative monoids; we show that the concepts of simpleness, congruence-simpleness, and ideal-simpleness for (complete) endomorphism semirings of projective semilattices (projective complete lattices) in the category of semilattices coincide iff those semilattices are finite distributive lattices; we also describe congruence-simple complete hemirings and left artinian congruence-simple complete hemirings. Considering the relationship between the concepts of "Morita equivalence" and "simpleness" in the semiring setting, we obtain the following further results: The ideal-simpleness, congruence-simpleness, and simpleness of semirings are Morita invariant properties; a complete description of simple semirings containing the infinite element; the "Double Centralizer Property" representation theorem for simple semirings; a complete description of simple semirings containing a projective minimal one-sided ideal; a characterization of ideal-simple semirings having either an infinite element or a projective minimal one-sided ideal; settling a conjecture and a problem as published by Katsov in 2004 for the classes of simple semirings containing either an infinite element or a projective minimal left (right) ideal, showing, respectively, that semirings of those classes are not perfect and that the concepts of "mono-flatness" and "flatness" for semimodules over semirings of those classes are the same. Finally, we give a complete description of ideal-simple, artinian additively idempotent chain semirings, as well as of congruence-simple, lattice-ordered semirings.

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13

Kearnes, Keith A. "Finite algebras that generate an injectively complete modular variety." Bulletin of the Australian Mathematical Society 44, no. 2 (October 1991): 303–24. http://dx.doi.org/10.1017/s0004972700029750.

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We extend Kollár's result on finitely generated, injectively complete congruence distributive varieties to the congruence modular setting. By doing so we show that, given any finite algebra A of finite type, there is an algorithm to decide whether V(A) is an injectively complete, congruence modular variety.

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14

Petrich, Mario. "The kernel relation for a strict extension of certain regular semigroups." Glasgow Mathematical Journal 38, no. 3 (September 1996): 347–57. http://dx.doi.org/10.1017/s0017089500031785.

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Let R be a regular semigroup and denote by (R) its congruence lattice. For , the kernel of pis the set ker . The relation K on (R) defined by λKp if ker λ = ker p is the kernel relation on (R). In general, K is a complete ∩-congruence but it is not a v-congruence. In view of the importance of the kernel-trace approach to the study of congruences on a regular semigroup (the trace of p is its restriction to idempotents of R), it is of considerable interest to determine necessary and sufficient conditions on R in order for K to be a congruence. This being in general a difficult task, one restricts attention to special classes of regular semigroups. For a background on this subject, consult [1].

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15

Kaarli, Kalle. "Locally finite affine complete varieties." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 62, no. 2 (April 1997): 141–59. http://dx.doi.org/10.1017/s1446788700000720.

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AbstractThe main results of the paper are the following: 1. Every locally finite affine complete variety admits a near unanimity term; 2. A locally finite congruence distributive variety is affine complete if and only if all its algebras with no proper subalgebras are affine complete and the variety is generated by one of such algebras. The first of these results sharpens a result of McKenzie asserting that all locally finite affine complete varieties are congruence distributive. The second one generalizes the result by Kaarli and Pixley that characterizes arithmetical affine complete varieties.

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16

Grätzer, G., and H. Lakser. "On congruence lattices of m-complete lattices." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 52, no. 1 (February 1992): 57–87. http://dx.doi.org/10.1017/s1446788700032869.

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AbstractThe lattice of all complete congruence relations of a complete lattice is itself a complete lattice. In an earlier paper, we characterize this lattice as a complete lattice. Let m be an uncountable regular cardinal. The lattice L of all m-complete congruence relations of an m-complete lattice K is an m-algebraic lattice; if K is bounded, then the unit element of L is m-compact. Our main result is the converse statement: For an m-algebraic lattice L with an m-compact unit element, we construct a bounded m-complete lattice K such that L is isomorphic to the lattice of m-complete congruence relations of K. In addition, if L has more than one element, then we show how to construct K so that it will also have a prescribed automorphism group. On the way to the main result, we prove a technical theorem, the One Point Extension Theorem, which is also used to provide a new proof of the earlier result.

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17

Pastijn, Francis. "The lattice of completely regular semigroup varieties." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 49, no. 1 (August 1990): 24–42. http://dx.doi.org/10.1017/s1446788700030214.

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AbstractA completely regular semigroup is a semigroup which is a union of groups. The class CR of completely regular semigroups forms a variety. On the lattice L (CR) of completely regular semigroup varieties we define two closure operations which induce complete congruences. The consideration of a third complete congruence on L (CR) yields a subdirect decomposition of L (CR). Using these results we show that L (CR) is arguesian. This confirms the (tacit) conjecture that L (CR) is modular.

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18

Czédli, Gábor. "Complete congruence lattices of two related modular lattices." Algebra universalis 78, no. 3 (September 27, 2017): 251–89. http://dx.doi.org/10.1007/s00012-017-0457-9.

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19

Gr�tzer, G., and E. T. Schmidt. "Complete congruence lattices of join-infinite distributive lattices." Algebra Universalis 37, no. 1 (January 1, 1997): 141–43. http://dx.doi.org/10.1007/s000120050008.

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20

Giacobazzi, Roberto, and Francesco Ranzato. "Correction to "Some properties of complete congruence lattices"." Algebra Universalis 47, no. 2 (June 1, 2002): 213. http://dx.doi.org/10.1007/s00012-002-8185-0.

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21

AUINGER, K., and T. E. HALL. "REPRESENTATIONS OF SEMIGROUPS BY TRANSFORMATIONS AND THE CONGRUENCE LATTICE OF AN EVENTUALLY REGULAR SEMIGROUP." International Journal of Algebra and Computation 06, no. 06 (December 1996): 655–85. http://dx.doi.org/10.1142/s0218196796000386.

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On any eventually regular semigroup S, congruences ν, μL, μR, μ, K, KL, KR, ζ are introduced which are the greatest congruences over: nil-extensions (n.e.) of completely simple semigroups, n.e. of left groups, n.e. of right groups, n.e. of groups, n.e. of rectangular bands, n.e. of left zero semigroups, n.e. of right zero semigroups, nil-semigroups, respectively. Each of these congruences is induced by a certain representation of S which is defined on an arbitrary semigroup. These congruences play an important role in the study of lattices of varieties, pseudovarieties and existence varieties. The investigation also leads to eight complete congruences U, Tt, Tr, T, K, Kl, Kr, Z on the congruence lattice Con (S) of S.

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22

Edwards, P. M. "On the lattice of congruences on an eventually regular semigroup." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 38, no. 2 (April 1985): 281–86. http://dx.doi.org/10.1017/s1446788700023144.

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AbstractA natural equivalence θ on the lattice of congruences λ(S) of a semigroup S is studied. For any eventually regular semigroup S, it is shown that θ is a congruence, each θ-class is a complete sublattice of λ(S) and the maximum element in each θ-class is determined. 1980 Mathematics subject classification (Amer. Math. Soc.): 20 M 10.

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23

Hofmann, K. H., and K. D. Magill. "The smallest proper congruence on S(X)." Glasgow Mathematical Journal 30, no. 3 (September 1988): 301–13. http://dx.doi.org/10.1017/s0017089500007394.

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S(X) is the semigroup of all continuous self maps of the topological space X and for any semigroup S, Cong(S) will denote the complete lattice of congruences on S. Cong(S) has a zero Z and a unit U. Specifically, Z = {(a, a):a ∈ S} and U = S × S. Evidently, Z and U are distinct if S has at least two elements. By a proper congruence on S we mean any congruence which differs from each of these. Since S(X) has more than one element when X is nondegenerate, we will assume without further mention that the spaces we discuss in this paper have more than one point. We observed in [4] that there are a number of topological spaces X such that S(X) has a largest proper congruence, that is, Cong(S(X)) has a unique dual atom which is greater than every other proper congruence on S(X). On the other hand, we also found out in [5] that it is also common for S(X) to fail to have a largest proper congruence. We will see that the situation is quite different at the other end of the spectrum in that it is rather rare for S(X) not to have a smallest proper congruence. In other words, for most spaces X, Cong(S(X)) has a unique atom which is smaller than every other proper congruence.

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24

Montanari, Ugo, and Vladimiro Sassone. "Dynamic Congruence vs. Progressing Bisimulation for CCS1." Fundamenta Informaticae 16, no. 2 (March 1, 1992): 171–99. http://dx.doi.org/10.3233/fi-1992-16206.

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Weak Observational Congruence (woc) defined on CCS agents is not a bisimulation since it does not require two states reached by bisimilar computations of woc agents to be still woc, e.g. α.τ.β.nil and α.β.nil are woc but τ.β.nil and β.nil are not. This fact prevent us from characterizing CCS semantics (when τ is considered invisible) as a final algebra, since the semantic function would induce an equivalence over the agents that is both a congruence and a bisimulation. In the paper we introduce a new behavioural equivalence for CCS agents, which is the coarsest among those bisimulations which are also congruences. We call it Dynamic Observational Congruence because it expresses a natural notion of equivalence for concurrent systems required to simulate each other in the presence of dynamic, i.e. run time, (re)configurations. We provide an algebraic characterization of Dynamic Congruence in terms of a universal property of finality. Furthermore we introduce Progressing Bisimulation, which forces processes to simulate each other performing explicit steps. We provide an algebraic characterization of it in terms of finality, two logical characterizations via modal logic in the style of HML and a complete axiomatization for finite agents (consisting of the axioms for Strong Observational Congruence and of two of the three Milner’s τ-laws). Finally, we prove that Dynamic Congruence and Progressing Bisimulation coincide for CCS agents.

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25

Kehayopulu, Niovi. "Ideals and Green's relations in ordered semigroups." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–8. http://dx.doi.org/10.1155/ijmms/2006/61286.

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Exactly as in semigroups, Green's relations play an important role in the theory of ordered semigroups—especially for decompositions of such semigroups. In this paper we deal with theℐ-trivial ordered semigroups which are defined via the Green's relationℐ, and with the nil andΔ-ordered semigroups. We prove that every nil ordered semigroup isℐ-trivial which means that there is no ordered semigroup which is 0-simple and nil at the same time. We show that in nil ordered semigroups which are chains with respect to the divisibility ordering, every complete congruence is a Rees congruence, and that this type of ordered semigroups are△-ordered semigroups, that is, ordered semigroups for which the complete congruences form a chain. Moreover, the homomorphic images of△-ordered semigroups are△-ordered semigroups as well. Finally, we prove that the ideals of a nil ordered semigroupSform a chain under inclusion if and only ifSis a chain with respect to the divisibility ordering.

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26

Picado, Jorge. "On complete congruence lattices of join-infinite distributive lattices." Algebra Universalis 44, no. 3-4 (December 1, 2000): 325–32. http://dx.doi.org/10.1007/s000120050191.

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27

Auinger, Karl. "The congruence lattice of a combinatorial strict inverse semigroup." Proceedings of the Edinburgh Mathematical Society 37, no. 1 (February 1994): 25–37. http://dx.doi.org/10.1017/s0013091500018654.

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28

Auinger, Karl. "Semigroups with atomistic congruence lattices." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 52, no. 1 (February 1992): 88–102. http://dx.doi.org/10.1017/s1446788700032870.

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AbstractIn this note a characterization of semigroups with atomistic consruence lattices, given for weakly reductive semigroups, is generalized to arbitrary semigroups. Also, it is shown that there is a complete congruence on the congruence lattice of such a semigroup that decomposes it into a disjoint union of intervals of the partition lattice.

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29

Xu, Hui, and Huaying Li. "Operationalize Interest Congruence: A Comparative Examination of Four Approaches." Journal of Career Assessment 28, no. 4 (March 9, 2020): 571–88. http://dx.doi.org/10.1177/1069072720909825.

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Although interest congruence is a cornerstone of career counseling, little is known about the relative importance of different operationalization approaches to interest congruence (i.e., how to calculate interest congruence). Using a sample of U.S. employees ( n = 303), the current study comparatively examined four profile-based conceptual congruence approaches, namely Euclidean distance, angular agreement, profile deviance, and profile correlation, in terms of their predictions for job and life satisfaction, turnover intention, and perceived person–job fit. The results found that profile correlation demonstrated complete dominance (i.e., ubiquitously stronger predictive utility) over the other three congruence indices in predicting all four career outcomes. Therefore, the current study portrays profile correlation as a preferred operationalization approach to interest congruence and offers rich implications for congruence research and practice.

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30

Milner, Robin. "A complete axiomatisation for observational congruence of finite-state behaviours." Information and Computation 81, no. 2 (May 1989): 227–47. http://dx.doi.org/10.1016/0890-5401(89)90070-9.

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31

Xiao, Qimei, and Qingguo Li. "Generalized Lower and Upper Approximations in Quantales." Journal of Applied Mathematics 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/648983.

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We introduce the concepts of set-valued homomorphism and strong set-valued homomorphism of a quantale which are the extended notions of congruence and complete congruence, respectively. The properties of generalized lower and upper approximations, constructed by a set-valued mapping, are discussed.

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32

Bai, Lili, and Hsin-Ya Liao. "The Relation Between Interest Congruence and College Major Satisfaction: Evidence From the Basic Interest Measures." Journal of Career Assessment 27, no. 4 (August 14, 2018): 628–44. http://dx.doi.org/10.1177/1069072718793966.

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The relation between the degree of interest congruence (i.e., person–environment fit in interest domain) and career satisfaction has been inconsistent and generally low across studies. Interest congruence is typically measured at the broadband general interest level, bound within Holland’s Realistic, Investigative, Artistic, Social, Enterprising, and Conventional (RIASEC) framework, and largely based on the match of the high-point interest codes between persons and environments. Using two cross-cultural college samples, we reexamined the congruence–satisfaction relation with a refined congruence index by using narrowband basic interest measures and considering the entire basic interest profiles. As a comparison, we used three additional congruence indices based on the entire general interest RIASEC profiles or the high-point RIASEC codes. Findings showed stronger congruence–satisfaction relations when the basic interest measure and/or complete interest profiles were used to generate interest congruence indices. Implications for research and career practice are discussed.

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33

Cristani, M. "The Complexity of Reasoning about Spatial Congruence." Journal of Artificial Intelligence Research 11 (November 20, 1999): 361–90. http://dx.doi.org/10.1613/jair.641.

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In the recent literature of Artificial Intelligence, an intensive research effort has been spent, for various algebras of qualitative relations used in the representation of temporal and spatial knowledge, on the problem of classifying the computational complexity of reasoning problems for subsets of algebras. The main purpose of these researches is to describe a restricted set of maximal tractable subalgebras, ideally in an exhaustive fashion with respect to the hosting algebras. In this paper we introduce a novel algebra for reasoning about Spatial Congruence, show that the satisfiability problem in the spatial algebra MC-4 is NP-complete, and present a complete classification of tractability in the algebra, based on the individuation of three maximal tractable subclasses, one containing the basic relations. The three algebras are formed by 14, 10 and 9 relations out of 16 which form the full algebra.

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34

Bergman, Clifford, and Ralph McKenzie. "Minimal varieties and quasivarieties." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 48, no. 1 (February 1990): 133–47. http://dx.doi.org/10.1017/s1446788700035266.

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AbstractWe prove that every locally finite, congruence modular, minimal variety is minimal as a quasivariety. We also construct all finite, strictly simple algebras generating a congruence distributive variety, such that the sett of unary term perations forms a group. Lastly, these results are applied to a problem in algebraic logic to give a sufficient condition for a deductive system to be structurally complete.

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35

Alaba, Berhanu Assaye, and Wondwosen Zemene Norahun. "Fuzzy Ideals and Fuzzy Filters of Pseudocomplemented Semilattices." Advances in Fuzzy Systems 2019 (July 8, 2019): 1–13. http://dx.doi.org/10.1155/2019/4263923.

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In this paper, we introduce the concept of kernel fuzzy ideals and ⁎-fuzzy filters of a pseudocomplemented semilattice and investigate some of their properties. We observe that every fuzzy ideal cannot be a kernel of a ⁎-fuzzy congruence and we give necessary and sufficient conditions for a fuzzy ideal to be a kernel of a ⁎-fuzzy congruence. On the other hand, we show that every fuzzy filter is the cokernel of a ⁎-fuzzy congruence. Finally, we prove that the class of ⁎-fuzzy filters forms a complete lattice that is isomorphic to the lattice of kernel fuzzy ideals.

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36

Hitchin, Rebecca, and Michael J. Benton. "Congruence between parsimony and stratigraphy: comparisons of three indices." Paleobiology 23, no. 1 (1997): 20–32. http://dx.doi.org/10.1017/s0094837300016626.

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Use of quantitative statistical tests can show that there is generally good congruence between estimated cladistic hypotheses of relationship and observed stratigraphy. A data set of 376 cladograms of fishes, continental tetrapods, and echinoderms was tested using three metrics, Spearman Rank Correlation (SRC), Relative Completeness Index (RCI), and Stratigraphic Consistency Index (SCI), to explore the relationships between the indices and differences in results among the three groups of organisms.There is a strong relationship between SCI and SRC, since both tests measure the same aspect of the fossil record. There is no relationship between RCI and either SCI or SRC. There is a highly significant relationship, as expected, between SRC coefficients and the number of taxa in a cladogram, but no such relationship for RCI or SCI (except in fishes). There is no significant relationship between any of the indices and either the number of internal nodes or tree balance.Echinoderms show the best stratigraphic consistency of nodes, while continental tetrapods have the best matching of stratigraphic age and cladistic node order. Fishes have the worst match of age and clade ranks, but they do have the most complete fossil record as measured by the RCI. They are followed by echinoderms, and then continental tetrapods, which have the least complete record. This seems to show that life in an aquatic environment leads, in general, to a more complete fossil record.

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Alemayehu, Teferi Getachew, Derso Abeje Engidaw, and Gezahagne Mulat Addis. "L-Fuzzy Congruences and L-Fuzzy Kernel Ideals in Ockham Algebras." Journal of Mathematics 2021 (June 19, 2021): 1–12. http://dx.doi.org/10.1155/2021/6644443.

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In this paper, we study fuzzy congruence relations and kernel fuzzy ideals of an Ockham algebra A , f , whose truth values are in a complete lattice satisfying the infinite meet distributive law. Some equivalent conditions are derived for a fuzzy ideal of an Ockham algebra A to become a fuzzy kernel ideal. We also obtain the smallest (respectively, the largest) fuzzy congruence on A having a given fuzzy ideal as its kernel.

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Kiss, Emil W. "An Easy Way to Minimal Algebras." International Journal of Algebra and Computation 07, no. 01 (February 1997): 55–75. http://dx.doi.org/10.1142/s021819679700006x.

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A finite algebra C is called minimal with respect to a pair δ<θ of its congruences if every unary polynomial f of C is either a permutation, or f(θ)⊆δ. It is the basic idea of tame congruence theory developed by Ralph McKenzie and David Hobby [7] to describe finite algebras via minimal algebras that sit inside them. As shown in [7] minimal algebras have a very restricted structure. This paper presents a new tool, the Twin Lemma, which makes it possible to give short proofs of some of these structure theorems. This part can be read as an alternative introduction to the theory. Our method yields new information in the type 1 case, and is especially useful in describing E-minimal algebras (that is, algebras that are minimal with respect to every prime congruence quotient). We complete their theory given in [7] by proving a structure theorem for the type 1 case. Finally we show that if an algebra is minimal with respect to two quotients, then the two types are the same, and if this type is 2, 3, or 4, then the bodies are also equal.

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Ferdinand, Augusty Tae. "Destination authentic value advantage: an SDL perspective." Management & Marketing. Challenges for the Knowledge Society 16, no. 2 (June 1, 2021): 101–17. http://dx.doi.org/10.2478/mmcks-2021-0007.

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Abstract This study aims to build a destination marketing conceptual model to bridge the research gap concerning managing a destination service-scape quality for enhancing destination loyalty. The convenience sample data were collected from an unknown population of Indonesian domestic tourists who visited tourist destinations in Indonesia. Data were analysed using AMOS SEM Software. The findings demonstrate the significant impacts of destination servicescape quality on destination authentic value advantage. The research findings resulted in a complete significant pathway to enhancing loyalty by mediating an authentic destination advantage through destination congruence. This study is evidence for the application of SDL-Service Dominant Logic Theory. The possibility of enhancing an authentic value experience superiority would be a strategic process for achieving any level of destination congruence as a step towards creating and sustaining loyalty. Destination planning could consider crafting the hardscape and soft-scape of a destination equally. A company should provide services that encourage positive emotions as the basis for building congruency. The originality of this study is the concept of destination servicescape quality with two new dimensions of destination service, hard-servicescape and soft-servicescape, and the development of destination authentic value advantage for enhancing authentic value advantage.

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Roy, Prof B. M. "RP-181: Formulation of Standard Quadratic Congruence of Even Composite Modulus modulo an Even Prime Raised to the Power n." International Journal for Research in Applied Science and Engineering Technology 9, no. 8 (August 31, 2021): 3064–69. http://dx.doi.org/10.22214/ijraset.2021.37870.

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Abstract: The paper presented here, is a standard quadratic congruence of composite modulus, studied rigorously and found the formulation incomplete. It was partially formulated by the earlier mathematicians. The present authors realised that the earlier formulation need a completion and a reformulation of the solutions is done along with two more results. The author considered the problem for reformulation, studied and reformulated the solutions completely. A partial formulation is found in a books of Number Theory by Zuckerman at el. There the formulation is only for an odd positive integer but nothing is said about even positive integer. The authors have provided a complete formulation of the said quadratic congruence and presented here. Keywords: Composite Modulus, Quadratic Congruence, Reformulation.

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FREESE, RALPH, and MATTHEW A. VALERIOTE. "ON THE COMPLEXITY OF SOME MALTSEV CONDITIONS." International Journal of Algebra and Computation 19, no. 01 (February 2009): 41–77. http://dx.doi.org/10.1142/s0218196709004956.

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This paper studies the complexity of determining if a finite algebra generates a variety that satisfies various Maltsev conditions, such as congruence distributivity or modularity. For idempotent algebras we show that there are polynomial time algorithms to test for these conditions but that in general these problems are EXPTIME complete. In addition, we provide sharp bounds in terms of the size of two-generated free algebras on the number of terms needed to witness various Maltsev conditions, such as congruence distributivity.

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Fang, Jie, and Lei-Bo Wang. "de Morgan algebras with double pseudocomplementation." Asian-European Journal of Mathematics 08, no. 01 (March 2015): 1550005. http://dx.doi.org/10.1142/s1793557115500059.

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We investigate de Morgan algebras with double pseudocomplementation. In particular, we characterize the congruence relations of such algebras, and provide a complete description of subdirectly irreducible members of this class.

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Mudrinski, Nebojša. "The largest higher commutator sequence." Reports on Mathematical Logic 54 (2019): 83–94. http://dx.doi.org/10.4467/20842589rm.19.004.10652.

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Given the congruence lattice L of a finite algebra A that generates a congruence permutable variety, we look for those sequences of operations on L that have the properties of higher commutator operations of expansions of A. If we introduce the order of such sequences in the natural way the question is whether exists or not the largest one. The answer is positive. We provide a description of the largest element and as a consequence we obtain that the sequences form a complete lattice.

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Koutny, Maciej. "Axiom System Induced by CTL* Logic." Fundamenta Informaticae 14, no. 2 (February 1, 1991): 235–53. http://dx.doi.org/10.3233/fi-1991-14205.

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We discuss some of the problems concerning bisimulation relations over behaviour expressions representing non-sequential systems. The kind of bisimulation we investigate is derived from the notion of bisimulation relation between two Kripke structures, which provides a full characterisation of semantical equivalence of such structures w.r.t. the CTL* branching time temporal logic without the next-time operator. This new bisimulation on behaviour expressions, called CTL*-bisimulation, induces a congruence on recursion-free behaviour expressions, and in this paper we derive a sound and complete axiom system for this congruence.

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Morelli, Federico, Zbigniew Kwieciński, Piotr Indykiewicz, Łukasz Jankowiak, Paweł Szymański, Petra Šímová, and Piotr Tryjanowski. "Congruence between breeding and wintering biodiversity hotspots: A case study in farmlands of Western Poland." European Journal of Ecology 4, no. 2 (January 1, 2019): 75–83. http://dx.doi.org/10.2478/eje-2018-0014.

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Abstract Farmland landscapes are recognized as important ecosystems, not only for their rich biodiversity but equally so for the human beings who live and work in these places. However, biodiversity varies among sites (spatial change) and among seasons (temporal change). In this work, we tested the hypothesis that bird diversity hotspots distribution for breeding is congruent with bird diversity hotspots for wintering season, focusing also the representation of protected areas for the conservation of local hotspots. We proposed a framework based on the use of species richness, functional diversity, and evolutionary distinctiveness to characterize avian communities. Although our findings show that the spatial distribution of local bird hotspots differed slightly between seasons, the protected areas’ representation was similar in both seasons. Protected areas covered 65% of the most important zones for breeding and 71% for the wintering season in the farmland studied. Functional diversity showed similar patterns as did bird species richness, but this measure can be most effective for highlighting differences on bird community composition. Evolutionary distinctiveness was less congruent with species richness and functional diversity, among seasons. Our findings suggest that inter-seasonal spatial congruence of local hotspots can be considered as suitable areas upon which to concentrate greater conservation efforts. However, even considering the relative congruence of avian diversity metrics at a local spatial scale, simultaneous analysis of protected areas while inter-seasonally considering hotspots, can provide a more complete representation of ecosystems for assessing the conservation status and designating priority areas.

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Gonzalez, Jorge A. "Demographic dissimilarity, value congruence, and workplace attachment." Journal of Managerial Psychology 31, no. 1 (February 8, 2016): 169–85. http://dx.doi.org/10.1108/jmp-07-2013-0256.

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Purpose – Relying on relational demography and person-organization fit perspectives, the purpose of this paper is to explore the interactive effect of demographic dissimilarity and value congruence on workplace attachment outcomes – affective and normative organizational commitment and turnover intentions. Based on optimal distinctiveness theory, asymmetrical effects across gender and race/ethnicity are also examined. Design/methodology/approach – A diverse sample of 278 restaurant workers in 30 different work units is used to test the hypotheses using hierarchical OLS regression. Findings – The results partially support the idea that perceived and objective value congruence moderate the relationship of race/ethnic and gender dissimilarity on workplace attachment. Tests for asymmetrical demographic group effects showed that value congruence had a stronger moderating effect for whites than for people of color, and for men than for women. Research limitations/implications – The results suggest that value congruence can ameliorate the adverse diversity effects on workplace attachment, but that a complete substitution effect may not be present. Women and minorities may still be sensitive to demographic representation even when their value congruence is high. This implies that a simultaneous pursuit of fit and diversity is an adequate diversity management strategy to stimulate the inclusion and workplace attachment of all social groups. Originality/value – This study joins a limited number of studies addressing the interaction of value congruence and demographic dissimilarity, and presents empirical evidence from a work setting. Also, this is the first study to show gender and race/ethnic differences in this interaction.

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Li, Fei, and Zhenliang Zhang. "The Homomorphisms and Operations of Rough Groups." Scientific World Journal 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/507972.

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Based on the light relation between a normal subgroup and a complete congruence relation of a group, we consider the homomorphism problem of rough groups and rough quotient groups and investigate their operational properties. Some new results are obtained.

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Petersen, Gitte, Ole Seberg, Frederick T. Short, and Miguel D. Fortes. "Complete genomic congruence but non-monophyly of Cymodocea (Cymodoceaceae), a small group of seagrasses." Taxon 63, no. 1 (February 1, 2014): 3–8. http://dx.doi.org/10.12705/631.2.

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Longstaff, W. E., J. B. Nation, and Oreste Panaia. "Abstract reflexive sublattices and completely distributive collapsibility." Bulletin of the Australian Mathematical Society 58, no. 2 (October 1998): 245–60. http://dx.doi.org/10.1017/s0004972700032226.

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There is a natural Galois connection between subspace lattices and operator algebras on a Banach space which arises from the notion of invariance. If a subspace lattice ℒ is completely distributive, then ℒ is reflexive. In this paper we study the more general situation of complete lattices for which the least complete congruence δ on ℒ such that ℒ/δ is completely distributive is well-behaved. Our results are purely lattice theoretic, but the motivation comes from operator theory.

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Shriner, Jeff. "Hardness results for the subpower membership problem." International Journal of Algebra and Computation 28, no. 05 (August 2018): 719–32. http://dx.doi.org/10.1142/s0218196718500339.

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The main result of this paper shows that if [Formula: see text] is a consistent strong linear Maltsev condition which does not imply the existence of a cube term, then for any finite algebra [Formula: see text] there exists a new finite algebra [Formula: see text] which satisfies the Maltsev condition [Formula: see text], and whose subpower membership problem is at least as hard as the subpower membership problem for [Formula: see text]. We characterize consistent strong linear Maltsev conditions which do not imply the existence of a cube term, and show that there are finite algebras in varieties that are congruence distributive and congruence [Formula: see text]-permutable ([Formula: see text]) whose subpower membership problem is EXPTIME-complete.

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