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Journal articles on the topic 'Associative rings'

Author: Grafiati

Published: 4 June 2021

Last updated: 28 July 2024

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1

Beidar, K. I., V. N. Latyshev, V. T. Markov, A. V. Mikhalev, L. A. Skornyakov, and A. A. Tuganbaev. "Associative rings." Journal of Soviet Mathematics 38, no. 3 (August 1987): 1855–929. http://dx.doi.org/10.1007/bf01093433.

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2

Feigelstock, Shalom. "E-Associative Rings." Canadian Mathematical Bulletin 36, no. 2 (June 1, 1993): 147–53. http://dx.doi.org/10.4153/cmb-1993-022-4.

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AbstractA ring R is E-associative if φ(xy) = φ(x)y for all endomorphisms φ of the additive group of R, and all x,y ∊ R. Unital E-associative rings are E-rings. The structure of the torsion ideal of an E-associative ring is described completely. The E-associative rings with completely decomposable torsion free additive groups are also classified. Conditions under which E-associative rings are E-rings, and other miscellaneous results are obtained.

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3

Belov, A. Ya. "On rings asymptotically close to associative rings." Siberian Advances in Mathematics 17, no. 4 (December 2007): 227–67. http://dx.doi.org/10.3103/s1055134407040013.

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4

Balaba, I. N., A. L. Kanunnikov, and A. V. Mikhalev. "Quotient rings of graded associative rings. I." Journal of Mathematical Sciences 186, no. 4 (September 23, 2012): 531–77. http://dx.doi.org/10.1007/s10958-012-1005-y.

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5

Waliyanti, Ida Kurnia, Indah Emilia Wijayanti, and M. Farchani Rosyid. "On Non-Associative Rings." Mathematics and Statistics 9, no. 2 (March 2021): 172–78. http://dx.doi.org/10.13189/ms.2021.090212.

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6

Kirichenko, V. V. "Quivers of Associative Rings." Journal of Mathematical Sciences 131, no. 6 (December 2005): 6032–51. http://dx.doi.org/10.1007/s10958-005-0459-6.

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7

García, J., and L. Marín. "WATTS THEOREMS FOR ASSOCIATIVE RINGS." Communications in Algebra 29, no. 12 (January 1, 2001): 5799–834. http://dx.doi.org/10.1081/agb-100107960.

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8

García, J., and L. Marín. "MORITA THEORY FOR ASSOCIATIVE RINGS." Communications in Algebra 29, no. 12 (January 1, 2001): 5835–56. http://dx.doi.org/10.1081/agb-100107961.

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9

Ashraf, Mohd, and Murtaza A. Quadri. "On commutativity of associative rings." Bulletin of the Australian Mathematical Society 38, no. 2 (October 1988): 267–71. http://dx.doi.org/10.1017/s0004972700027544.

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10

Zlydnev, D. V. "Associative rings with large center." Journal of Mathematical Sciences 191, no. 5 (May 17, 2013): 691–93. http://dx.doi.org/10.1007/s10958-013-1352-3.

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11

Celikbas, Olgur, Lars Winther Christensen, Li Liang, and Greg Piepmeyer. "Complete homology over associative rings." Israel Journal of Mathematics 221, no. 1 (September 2017): 1–24. http://dx.doi.org/10.1007/s11856-017-1562-3.

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12

Bahturin, Y. A., and M. V. Zaicev. "Semigroup gradings on associative rings." Advances in Applied Mathematics 37, no. 2 (August 2006): 153–61. http://dx.doi.org/10.1016/j.aam.2005.06.009.

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13

Celikbas, Olgur, Lars Winther Christensen, Li Liang, and Greg Piepmeyer. "Stable homology over associative rings." Transactions of the American Mathematical Society 369, no. 11 (March 30, 2017): 8061–86. http://dx.doi.org/10.1090/tran/6897.

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14

Mikhalev, A. V. "MULTIPLICATIVE CLASSIFICATION OF ASSOCIATIVE RINGS." Mathematics of the USSR-Sbornik 63, no. 1 (February 28, 1989): 205–18. http://dx.doi.org/10.1070/sm1989v063n01abeh003268.

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15

Bhavanari, Satyanarayana, Nagaraju Dasari, Balamurugan Kuppareddy Subramanyam, and Godloza Lungisile. "Finite Dimension in Associative Rings." Kyungpook mathematical journal 48, no. 1 (March 31, 2008): 37–43. http://dx.doi.org/10.5666/kmj.2008.48.1.037.

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16

Holm, Henrik, and Diana White. "Foxby equivalence over associative rings." Journal of Mathematics of Kyoto University 47, no. 4 (2007): 781–808. http://dx.doi.org/10.1215/kjm/1250692289.

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17

Andruszkiewicz, R. R., and E. R. Puczylowski. "Kurosh's chains of associative rings." Glasgow Mathematical Journal 32, no. 1 (January 1990): 67–69. http://dx.doi.org/10.1017/s001708950000906x.

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Let N be a homomorphically closed class of associative rings. Put N1 = Nl = N and, for ordinals a ≥ 2, define Nα (Nα) to be the class of all associative rings R such that every non-zero homomorphic image of R contains a non-zero ideal (left ideal) in Nβ for some β<α. In this way we obtain a chain {Nα} ({Nα}), the union of which is equal to the lower radical class IN (lower left strong radical class IsN) determined by N. The chain {Nα} is called Kurosh's chain of N. Suliński, Anderson and Divinsky proved [7] that . Heinicke [3] constructed an example of N for which lN ≠ Nk for k = 1, 2,. … In [1] Beidar solved the main problem in the area showing that for every natural number n ≥ 1 there exists a class N such that IN = Nn+l ≠ Nn. Some results concerning the termination of the chain {Nα} were obtained in [2,4]. In this paper we present some classes N with Nα = Nα for all α Using this and Beidar's example we prove that for every natural number n ≥ 1 there exists an N such that Nα = Nα for all α and Nn ≠ Nn+i = Nn+2. This in particular answers Question 6 of [4].

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18

Garkusha, Grigory. "Homotopy theory of associative rings." Advances in Mathematics 213, no. 2 (August 2007): 553–99. http://dx.doi.org/10.1016/j.aim.2006.12.013.

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19

Nowakowska, M., and E. R. Puczyłowski. "Veldsman’s classes of associative rings." Acta Mathematica Hungarica 146, no. 2 (May 8, 2015): 466–95. http://dx.doi.org/10.1007/s10474-015-0506-9.

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20

EDMUNDS, CHARLES C. "INTERCHANGE RINGS." Journal of the Australian Mathematical Society 101, no. 3 (May 12, 2016): 310–34. http://dx.doi.org/10.1017/s1446788716000112.

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An interchange ring,$(R,+,\bullet )$, is an abelian group with a second binary operation defined so that the interchange law$(w+x)\bullet (y+z)=(w\bullet y)+(x\bullet z)$ holds. An interchange near ring is the same structure based on a group which may not be abelian. It is shown that each interchange (near) ring based on a group $G$ is formed from a pair of endomorphisms of $G$ whose images commute, and that all interchange (near) rings based on $G$ can be characterized in this manner. To obtain an associative interchange ring, the endomorphisms must be commuting idempotents in the endomorphism semigroup of $G$. For $G$ a finite abelian group, we develop a group-theoretic analogue of the simultaneous diagonalization of idempotent linear operators and show that pairs of endomorphisms which yield associative interchange rings can be diagonalized and then put into a canonical form. A best possible upper bound of $4^{r}$ can be given for the number of distinct isomorphism classes of associative interchange rings based on a finite abelian group $A$ which is a direct sum of $r$ cyclic groups of prime power order. If $A$ is a direct sum of $r$ copies of the same cyclic group of prime power order, we show that there are exactly ${\textstyle \frac{1}{6}}(r+1)(r+2)(r+3)$ distinct isomorphism classes of associative interchange rings based on $A$. Several examples are given and further comments are made about the general theory of interchange rings.

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21

Bharathi, D., and M. Munirathnam. "SIMPLE ASSOSYMMETRIC RINGS." Asian-European Journal of Mathematics 06, no. 04 (December 2013): 1350047. http://dx.doi.org/10.1142/s1793557113500472.

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In Kleinfeld [Assosymmetric rings, Proc. Amer. Math. Soc.8 (1957) 983–986] showed that every commutator and every associator is in the nucleus N. In this paper, first we prove that the nucleus coincides with the center of the ring. Using this result and results of Kleinfeld, it is shown that a simple assosymmetric ring is third power associative and hence associative.

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22

Markov, Viktor T., and Askar A. Tuganbaev. "Centrally essential rings which are not necessarily unital or associative." Discrete Mathematics and Applications 29, no. 4 (August 27, 2019): 215–18. http://dx.doi.org/10.1515/dma-2019-0019.

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Abstract Centrally essential rings were defined earlier for associative unital rings; in this paper, we define them for rings which are not necessarily associative or unital. In this case, it is proved that centrally essential semiprime rings are commutative. It is proved that all idempotents of a centrally essential alternative ring are central. Several examples of non-commutative centrally essential rings are provided, some properties of centrally essential rings are described.

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23

Beslin, Scott J., and Awad Iskander. "On the mappingxy→(xy)nin an associative ring." International Journal of Mathematics and Mathematical Sciences 2004, no. 26 (2004): 1393–96. http://dx.doi.org/10.1155/s0161171204208250.

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We consider the following condition (*) on an associative ringR:(*). There exists a functionffromRintoRsuch thatfis a group homomorphism of(R,+),fis injective onR2, andf(xy)=(xy)n(x,y)for some positive integern(x,y)>1. Commutativity and structure are established for Artinian ringsRsatisfying (*), and a counterexample is given for non-Artinian rings. The results generalize commutativity theorems found elsewhere. The casen(x,y)=2is examined in detail.

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24

Vukman, Joso, and Irena Kosi-Ulbl. "On dependent elements in rings." International Journal of Mathematics and Mathematical Sciences 2004, no. 54 (2004): 2895–906. http://dx.doi.org/10.1155/s0161171204311221.

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LetRbe an associative ring. An elementa∈Ris said to be dependent on a mappingF:R→Rin caseF(x)a=axholds for allx∈R. In this paper, elements dependent on certain mappings on prime and semiprime rings are investigated. We prove, for example, that in case we have a semiprime ringR, there are no nonzero elements which are dependent on the mappingα+β, whereαandβare automorphisms ofR.

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25

Poole, David G., and Patrick N. Stewart. "Classical quotient rings of generalized matrix rings." International Journal of Mathematics and Mathematical Sciences 18, no. 2 (1995): 311–16. http://dx.doi.org/10.1155/s0161171295000391.

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An associative ringRwith identity is a generalized matrix ring with idempotent setEifEis a finite set of orthogonal idempotents ofRwhose sum is1. We show that, in the presence of certain annihilator conditions, such a ring is semiprime right Goldie if and only ifeReis semiprime right Goldie for alle∈E, and we calculate the classical right quotient ring ofR.

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26

Tumurbat, S., T. Khulan, and D. Dayantsolmon. "A note on radicals of associative rings and alternative rings." Miskolc Mathematical Notes 23, no. 1 (2022): 175. http://dx.doi.org/10.18514/mmn.2022.2601.

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27

K. Subhashini, M. Shiva Sankar Reddy, and V. Raghavendra Prasad. "Alternative Derivations in (1,1) Rings." Journal of Advanced Zoology 44, no. 4 (December 1, 2023): 947–49. http://dx.doi.org/10.17762/jaz.v44i4.2385.

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Objectives: To show the associativity in one of the subclass of non-associative (γ,δ) rings. Method: Derivation alternator rings are limiting case of associative rings. The ring (1,1) is one of the sub class of (γ,δ) rings. Consider a (1,1) derivation alternator ring R, with characteristic ≠ 2, and it is well known that this ring is neither alternative nor flexible. In this paper it will be proved that right alternative property (R,x,x) holds in R and flexibility follows, finally associativity arrives in R. Findings: If this ring R does not contain nilpotent elements even though it will be associative. Novelty: Further investigators may extend the applications of these rings in science and engineering fields. Mathematics Subject Classification: 2010 MSC 17D

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28

Shah, Tariq, Nasreen Kausar, and Inayatur Rehman. "Intuitionistic Fuzzy Normal subrings over a non-associative ring." Analele Universitatii "Ovidius" Constanta - Seria Matematica 20, no. 1 (May 1, 2012): 369–86. http://dx.doi.org/10.2478/v10309-012-0025-4.

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Abstract N. Palaniappan et. al [20, 28] have investigated the concept of intuitionistic fuzzy normal subrings in associative rings. In this study we extend these notions for a class of non-associative rings

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29

Pavlova, T. V. "Corrigendum: Minimally complete associative Artinian rings." Sibirskie Elektronnye Matematicheskie Izvestiya 16 (December 13, 2019): 1913–15. http://dx.doi.org/10.33048/semi.2019.16.136.

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30

Cohn, P. M. "AUTOMORPHISMS AND DERIVATIONS OF ASSOCIATIVE RINGS." Bulletin of the London Mathematical Society 24, no. 6 (November 1992): 615–16. http://dx.doi.org/10.1112/blms/24.6.615.

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31

LANSKI, CHARLES. "FINITE HIGHER COMMUTATORS IN ASSOCIATIVE RINGS." Bulletin of the Australian Mathematical Society 89, no. 3 (September 27, 2013): 503–9. http://dx.doi.org/10.1017/s0004972713000890.

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AbstractIf $T$ is any finite higher commutator in an associative ring $R$, for example, $T= [[R, R] , [R, R] ] $, and if $T$ has minimal cardinality so that the ideal generated by $T$ is infinite, then $T$ is in the centre of $R$ and ${T}^{2} = 0$. Also, if $T$ is any finite, higher commutator containing no nonzero nilpotent element then $T$ generates a finite ideal.

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32

Mora, Teo. "Zacharias representation of effective associative rings." Journal of Symbolic Computation 99 (July 2020): 147–88. http://dx.doi.org/10.1016/j.jsc.2019.04.002.

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33

Andruszkiewicz, R. R. "On accessible subrings of associative rings." Proceedings of the Edinburgh Mathematical Society 35, no. 1 (February 1992): 101–7. http://dx.doi.org/10.1017/s0013091500005356.

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We describe for every natural n the class of rings R such that if R is an accessible (left accessible) subring of a ring then R is an n-accessible (n-left-accessible) subring of the ring. This is connected with the problem of the termination of Kurosh's construction of the lower (lower strong) radical. The result for n = 2 was obtained by Sands in a connection with some other questions.

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34

Riley, D. M., and Mark C. Wilson. "Associative rings satisfying the Engel condition." Proceedings of the American Mathematical Society 127, no. 4 (1999): 973–76. http://dx.doi.org/10.1090/s0002-9939-99-04643-2.

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35

Ougen, Xi. "Quasi-P radicals of associative rings." Acta Mathematica Hungarica 60, no. 1-2 (1992): 115–18. http://dx.doi.org/10.1007/bf00051763.

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36

Amberg, Bernhard, and Yaroslav Sysak. "Associative rings with metabelian adjoint group." Journal of Algebra 277, no. 2 (July 2004): 456–73. http://dx.doi.org/10.1016/j.jalgebra.2004.02.028.

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37

Fay, Temple H., and Stephan V. Joubert. "Categorical compactness for rings." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 59, no. 3 (December 1995): 313–29. http://dx.doi.org/10.1017/s1446788700037228.

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AbstractIn this paper we study categorical compactness with respect to a class of objects F being motiveated by examples arising from modules, abelian groups, and various classes of non-abelian groups. This theory is then applied to the category of not necessarily associative rings. In particular, we study the example arising from the class of all torsion-free rings. This work extends some recent results of B. J. Gardner for associative rings and radical classes.

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38

Kelathaya, Umashankara, and Manjunatha Prasad Karantha. "Reverse order law for outer inverses and Moore-Penrose inverse in the context of star order." F1000Research 11 (July 27, 2022): 843. http://dx.doi.org/10.12688/f1000research.123411.1.

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The reverse order law for outer inverses and the Moore-Penrose inverse is discussed in the context of associative rings. A class of pairs of outer inverses that satisfy reverse order law is determined. The notions of left-star and right-star orders have been extended to the case of arbitrary associative rings with involution and many of their interesting properties are explored. The distinct behavior of projectors in association with the star, right-star, and left-star partial orders led to several equivalent conditions for the reverse order law for the Moore-Penrose inverse.

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39

ANDRUSZKIEWICZ, RYSZARD R., and MAGDALENA SOBOLEWSKA. "ACCESSIBLE SUBRINGS AND KUROSH’S CHAINS OF ASSOCIATIVE RINGS." Journal of the Australian Mathematical Society 95, no. 2 (July 18, 2013): 145–57. http://dx.doi.org/10.1017/s1446788713000268.

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AbstractThis article is devoted to the historical study of the ADS-problem with a special emphasis on the use of methods and techniques, emerging with the development of the theory of rings: accessible subrings, iterated maximal essential extensions of rings, completely normal rings. We construct new examples of classes for which Kurosh’s chain stabilizes at any given step. We recall the old nontrivial questions, and we pose a new one.

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40

Hari babu, K., and K. Jayalakshmi. "(–1, 1) Rings without Nilpotent Elements." International Journal of Engineering & Technology 7, no. 4.10 (October 2, 2018): 387. http://dx.doi.org/10.14419/ijet.v7i4.10.20943.

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A ring of type 12(خ³,خ´)"> , was introduced by Albert and Kokoris [1,3] where in they have shown that a simple ring of 12(خ³,خ´)"> type is either associative or contains no idempotent other than 1. In this paper we obtain further results on the residual cases, to prove that a nonassociative (-1,1) rings satisfying (x, x, y)2 = 0, for all elements of the rings imply (x, x, y) = 0. But then indeed (-1,1) rings which have no nilpotent elements are associative and there by all such rings are division rings.

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41

Isbell, John. "Book Review: Cogroups and co-rings in categories of associative rings." Bulletin of the American Mathematical Society 34, no. 03 (July 1, 1997): 317–22. http://dx.doi.org/10.1090/s0273-0979-97-00719-2.

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42

Volkov, M. V. "Varieties of associative rings in which all critical rings are basic." Siberian Mathematical Journal 34, no. 1 (1992): 30–36. http://dx.doi.org/10.1007/bf00971238.

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43

France-Jackson, Halina. "On coatoms of the lattice of matric-extensible radicals." Bulletin of the Australian Mathematical Society 72, no. 3 (December 2005): 403–6. http://dx.doi.org/10.1017/s0004972700035231.

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A radical α in the universal class of all associative rings is called matric-extensible if for all natural numbers n and all rings A, A ∈ α if and only if Mn(A) ∈ α, where Mn(A) denotes the n × n matrix ring with entries from A. We show that there are no coatoms, that is, maximal elements in the lattice of all matric-extensible radicals of associative rings.

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44

Kelarev, A. V. "Hereditary radicals and bands of associative rings." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 51, no. 1 (August 1991): 62–72. http://dx.doi.org/10.1017/s1446788700033309.

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AbstractBands of associative rings were introduced in 1973 by Weissglass. For the radicals playing most essential roles in the structure theory (in particular, for those of Jacobson, Baer, Levitsky, Koethe) it is shown how to find the radical of a band of rings. The technique of the general Kurosh-Amitsur radical theory is used to consider many radicals simultaneously.

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45

DART, BRADLEY C., and EDGAR G. GOODAIRE. "LOOP RINGS SATISFYING IDENTITIES OF BOL–MOUFANG TYPE." Journal of Algebra and Its Applications 08, no. 03 (June 2009): 401–11. http://dx.doi.org/10.1142/s0219498809003394.

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The existence of loop rings that are not associative but which satisfy the Moufang or Bol identities is well known. Here we complete work started 25 years ago by establishing the existence of loop rings that satisfy any identity of "Bol–Moufang" type (without being associative). As it turns out, with one exception, loop rings satisfying an identity of Bol–Moufang type all satisfy a Moufang or Bol identity. We also highlight some similarities and differences in the consequences of several Bol–Moufang identities as they apply to loops and rings.

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46

Shah, Syed Tariq, Asima Razzaque, Inayatur Rehman, Muhammad Asif Gondal, Muhammad Iftikhar Faraz, and Kar Ping Shum. "Literature Survey on Non-Associative Rings and Developments." European Journal of Pure and Applied Mathematics 12, no. 2 (April 29, 2019): 370–408. http://dx.doi.org/10.29020/nybg.ejpam.v12i2.3408.

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In this paper we present a comprehensive survey and developments of existing literature of non-associative rings and enumerate some of their various applications in different directions to date. These applications explain the voluminous work in different fields of non-associative rings and through which various algebraic structures in theoretical point of view could be developed.

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47

Hashemi, E., R. Amirjan, and A. Alhevaz. "On zero-divisor graphs of skew polynomial rings over non-commutative rings." Journal of Algebra and Its Applications 16, no. 03 (March 2017): 1750056. http://dx.doi.org/10.1142/s0219498817500566.

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In this paper, we continue to study zero-divisor properties of skew polynomial rings [Formula: see text], where [Formula: see text] is an associative ring equipped with an endomorphism [Formula: see text] and an [Formula: see text]-derivation [Formula: see text]. For an associative ring [Formula: see text], the undirected zero-divisor graph of [Formula: see text] is the graph [Formula: see text] such that the vertices of [Formula: see text] are all the nonzero zero-divisors of [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are connected by an edge if and only if [Formula: see text] or [Formula: see text]. As an application of reversible rings, we investigate the interplay between the ring-theoretical properties of a skew polynomial ring [Formula: see text] and the graph-theoretical properties of its zero-divisor graph [Formula: see text]. Our goal in this paper is to give a characterization of the possible diameters of [Formula: see text] in terms of the diameter of [Formula: see text], when the base ring [Formula: see text] is reversible and also have the [Formula: see text]-compatible property. We also completely describe the associative rings all of whose zero-divisor graphs of skew polynomials are complete.

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48

McDougall, Robert. "A generalisation of the lower radical class." Bulletin of the Australian Mathematical Society 59, no. 1 (February 1999): 139–46. http://dx.doi.org/10.1017/s000497270003269x.

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In this work we demonstrate that the lower radical class construction on a homomorphically closed class of associative rings generates a radical class for any class of associative rings. We also give a new description of the upper radical class using the construction on an appropriate generating class.

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49

Woronowicz, Mateusz. "A Note on the Square Subgroups of Decomposable Torsion-Free Abelian Groups of Rank Three." Annales Mathematicae Silesianae 32, no. 1 (September 1, 2018): 319–31. http://dx.doi.org/10.1515/amsil-2017-0009.

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Abstract A hypothesis stated in [16] is confirmed for the case of associative rings. The answers to some questions posed in the mentioned paper are also given. The square subgroup of a completely decomposable torsion-free abelian group is described (in both cases of associative and general rings). It is shown that for any such a group A, the quotient group modulo the square subgroup of A is a nil-group. Some results listed in [16] are generalized and corrected. Moreover, it is proved that for a given abelian group A, the square subgroup of A considered in the class of associative rings, is a characteristic subgroup of A.

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50

Rashedi, Fatemeh. "Uniquely exchange rings." Publications de l'Institut Math?matique (Belgrade) 112, no. 126 (2022): 53–57. http://dx.doi.org/10.2298/pim2226053r.

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An associative ring with unity is called exchange if every element is exchange, i.e., there exists an idempotent e ? aR such that 1?e ? (1?a)R; if this representation is unique for every element, we call the ring uniquely exchange. We give a complete description of uniquely exchange rings.

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