Academic literature on the topic 'Regular semigroup'

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Journal articles on the topic "Regular semigroup"

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Luo, Xiao Qiang. "Π*-Regular Semigroups." Bulletin of Mathematical Sciences and Applications 1 (August 2012): 46–51. http://dx.doi.org/10.18052/www.scipress.com/bmsa.1.46.

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El-Qallali, Abdulsalam. "Left regular bands of groups of left quotients." Glasgow Mathematical Journal 33, no. 1 (January 1991): 29–40. http://dx.doi.org/10.1017/s0017089500008004.

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In this paper we characterize semigroups S which have a semigroup Q of left quotients, where Q is an ℛ-unipotent semigroup which is a band of groups. Recall that an ℛ-unipotent (or left inverse) semigroup S is one in which every ℛ-class contains a unique idempotent. It is well-known that any ℛ-unipotent semigroup 5 is a regular semigroup in which the set of idempotents is a left regular band in that efe = ef for any idempotents e, fin S. ℛ-unipotent semigroups were studied by several authors, see for example [1] and [13].Bailes [1]characterized ℛ-unipotent semigroups which are bands of groups. This characterization extended the structure of inverse semigroups which are semilattices of groups. Recently, Gould studied in [7]the semigroup S which has a semigroup Q of left quotients where Q is an inverse semigroup which is a semilattice of groups.
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Et. al., Dr D. Mrudula Devi. "A characterization of Commutative Semigroups." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 3 (April 11, 2021): 5150–55. http://dx.doi.org/10.17762/turcomat.v12i3.2065.

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This paper deals with some results on commutative semigroups. We consider (s,.) is externally commutative right zero semigroup is regular if it is intra regular and (s,.) is externally commutative semigroup then every inverse semigroup is u – inverse semigroup. We will also prove that if (S,.) is a H - semigroup then weakly cancellative laws hold in H - semigroup. In one case we will take (S,.) is commutative left regular semi group and we will prove that (S,.) is ∏ - inverse semigroup. We will also consider (S,.) is commutative weakly balanced semigroup and then prove every left (right) regular semigroup is weakly separate, quasi separate and separate. Additionally, if (S,.) is completely regular semigroup we will prove that (S,.) is permutable and weakly separtive. One a conclusing note we will show and prove some theorems related to permutable semigroups and GC commutative Semigroups.
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KANTOROVITZ, SHMUEL. "GENERATORS OF REGULAR SEMIGROUPS." Glasgow Mathematical Journal 50, no. 1 (January 2008): 47–53. http://dx.doi.org/10.1017/s0017089507003916.

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AbstractA regular semigroup (cf. [4, p. 38]) is a C0-semigroup T(⋅) that has an extension as a holomorphic semigroup W(⋅) in the right halfplane $\Bbb C^+$, such that ||W(⋅)|| is bounded in the ‘unit rectangle’ Q:=(0, 1]× [−1, 1]. The important basic facts about a regular semigroup T(⋅) are: (i) it possesses a boundary groupU(⋅), defined as the limit lims → 0+W(s+i⋅) in the strong operator topology; (ii) U(⋅) is a C0-group, whose generator is iA, where A denotes the generator of T(⋅); and (iii) W(s+it)=T(s)U(t) for all s+it ∈$\Bbb C^+$ (cf. Theorems 17.9.1 and 17.9.2 in [3]). The following converse theorem is proved here. Let A be the generator of a C0-semigroup T(⋅). If iA generates a C0-group, U(⋅), then T(⋅) is a regular semigroup, and its holomorphic extension is given by (iii). This result is related to (but not included in) known results of Engel (cf. Theorem II.4.6 in [2]), Liu [7] and the author [6] for holomorphic extensions into arbitrary sectors, of C0-semigroups that are bounded in every proper subsector. The method of proof is also different from the method used in these references. Criteria for generators of regular semigroups follow as easy corollaries.
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Kelarev, A. V. "The regular radical of semigroup rings of commutative semigroups." Glasgow Mathematical Journal 34, no. 2 (May 1992): 133–41. http://dx.doi.org/10.1017/s001708950000865x.

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A description of regular group rings is well known (see [12]). Various authors have considered regular semigroup rings (see [17], [8], [10], [11], [4]). These rings have been characterized for many important classes of semigroups, although the general problem turns out to be rather difficult and still has not got a complete solution. It seems natural to describe the regular radical in semigroup rings for semigroups of the classes mentioned. In [10], the regular semigroup rings of commutative semigroups were described. The aim of the present paper is to characterize the regular radical ρ(R[S]) for each associative ring R and commutative semigroup S.
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Shoji, Kunitaka. "Regular Semigroups Which Are Amalgamation Bases for Finite Semigroups." Algebra Colloquium 14, no. 02 (June 2007): 245–54. http://dx.doi.org/10.1142/s1005386707000247.

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In this paper, we prove that a completely 0-simple (or completely simple) semigroup is an amalgamation base for finite semigroups if and only if it is an amalgamation base for semigroups. By adopting the same method as used in a previous paper, we prove that a finite regular semigroup is an amalgamation base for finite semigroups if its [Formula: see text]-classes are linearly ordered and all of its principal factor semigroups are amalgamation bases for finite semigroups. Finally, we give an example of a finite semigroup U which is an amalgamation base for semigroups, but not all of its principal factor semigroups are amalgamation bases either for semigroups or for finite semigroups.
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NI, XIANGFEI, and HAIZHOU CHAO. "REGULAR SEMIGROUPS WITH NORMAL IDEMPOTENTS." Journal of the Australian Mathematical Society 103, no. 1 (March 29, 2017): 116–25. http://dx.doi.org/10.1017/s1446788717000088.

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In this paper, we investigate regular semigroups that possess a normal idempotent. First, we construct a nonorthodox nonidempotent-generated regular semigroup which has a normal idempotent. Furthermore, normal idempotents are described in several different ways and their properties are discussed. These results enable us to provide conditions under which a regular semigroup having a normal idempotent must be orthodox. Finally, we obtain a simple method for constructing all regular semigroups that contain a normal idempotent.
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Wang, Shoufeng. "On E-semiabundant semigroups with a multiplicative restriction transversal." Studia Scientiarum Mathematicarum Hungarica 55, no. 2 (June 2018): 153–73. http://dx.doi.org/10.1556/012.2018.55.2.1374.

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Multiplicative inverse transversals of regular semigroups were introduced by Blyth and McFadden in 1982. Since then, regular semigroups with an inverse transversal and their generalizations, such as regular semigroups with an orthodox transversal and abundant semigroups with an ample transversal, are investigated extensively in literature. On the other hand, restriction semigroups are generalizations of inverse semigroups in the class of non-regular semigroups. In this paper we initiate the investigations of E-semiabundant semigroups by using the ideal of "transversals". More precisely, we first introduce multiplicative restriction transversals for E-semiabundant semigroups and obtain some basic properties of E-semiabundant semigroups containing a multiplicative restriction transver- sal. Then we provide a construction method for E-semiabundant semigroups containing a multiplicative restriction transversal by using the Munn semigroup of an admissible quadruple and a restriction semigroup under some natural conditions. Our construction is similar to Hall's spined product construction of an orthodox semigroup. As a corollary, we obtain a new construction of a regular semigroup with a multiplicative inverse transversal and an abundant semigroup having a multiplicative ample transversal, which enriches the corresponding results obtained by Blyth-McFadden and El-Qallali, respectively.
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GIGOŃ, ROMAN S. "REGULAR CONGRUENCES ON AN IDEMPOTENT-REGULAR-SURJECTIVE SEMIGROUP." Bulletin of the Australian Mathematical Society 88, no. 2 (July 30, 2013): 190–96. http://dx.doi.org/10.1017/s0004972713000270.

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AbstractA semigroup $S$ is called idempotent-surjective (respectively, regular-surjective) if whenever $\rho $ is a congruence on $S$ and $a\rho $ is idempotent (respectively, regular) in $S/ \rho $, then there is $e\in {E}_{S} \cap a\rho $ (respectively, $r\in \mathrm{Reg} (S)\cap a\rho $), where ${E}_{S} $ (respectively, $\mathrm{Reg} (S)$) denotes the set of all idempotents (respectively, regular elements) of $S$. Moreover, a semigroup $S$ is said to be idempotent-regular-surjective if it is both idempotent-surjective and regular-surjective. We show that any regular congruence on an idempotent-regular-surjective (respectively, regular-surjective) semigroup is uniquely determined by its kernel and trace (respectively, the set of equivalence classes containing idempotents). Finally, we prove that all structurally regular semigroups are idempotent-regular-surjective.
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Lawson, M. V. "Enlargements of regular semigroups." Proceedings of the Edinburgh Mathematical Society 39, no. 3 (October 1996): 425–60. http://dx.doi.org/10.1017/s001309150002321x.

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We introduce a class of regular extensions of regular semigroups, called enlargements; a regular semigroup T is said to be an enlargement of a regular subsemigroup S if S = STS and T = TST. We show that S and T have many properties in common, and that enlargements may be used to analyse a number of questions in regular semigroup theory.
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Dissertations / Theses on the topic "Regular semigroup"

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Wilcox, Stewart. "Cellularity of Twisted Semigroup Algebras of Regular Semigroups." University of Sydney. Mathematics and Statistics, 2006. http://hdl.handle.net/2123/720.

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There has been much interest in algebras which have a basis consisting of diagrams, which are multiplied in some natural diagrammatic way. Examples of these so-called diagram algebras include the partition, Brauer and Temperley-Lieb algebras. These three examples all have the property that the product of two diagram basis elements is always a scalar multiple of another basis element. Motivated by this observation, we find that these algebras are examples of twisted semigroup algebras. Such algebras are an obvious extension of twisted group algebras, which arise naturally in various contexts; examples include the complex numbers and the quaternions, considered as algebras over the real numbers. The concept of a cellular algebra was introduced in a famous paper of Graham and Lehrer; an algebra is called cellular if it has a basis of a certain form, in which case the general theory of cellular algebras allows us to easily derive information about the semisimplicity of the algebra and about its representation theory, even in the non-semisimple case. Many diagram algebras (including the above three examples) are known to be cellular. The aim of this thesis is to deduce the cellularity of these examples (and others) by proving a general result about the cellularity of twisted semigroup algebras. This will extend a recent result of East. In Chapters 2 and 3 we discuss semigroup theory and twisted semigroup algebras, and realise the above three examples as twisted semigroup algebras. Chapters 4 to 7 detail and extend slightly the theory of cellular algebras. In Chapter 8 we state and prove the main theorem, which shows that certain twisted semigroup algebras are cellular. Under the assumptions of the main theorem, we explore the cell representations of twisted semigroup algebras in Chapter 9. Finally in Chapter 10, we apply the theorem to various examples, including the three diagram algebras mentioned above.
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Wilcox, Stewart. "Cellularity of twisted semigroup algebras of regular semigroups /." Connect to full text, 2005. http://hdl.handle.net/2123/720.

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Sondecker, Victoria L. "Kernel-trace approach to congruences on regular and inverse semigroups." Instructions for remote access. Click here to access this electronic resource. Access available to Kutztown University faculty, staff, and students only, 1994. http://www.kutztown.edu/library/services/remote_access.asp.

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Thesis (M.A.)--Kutztown University of Pennsylvania, 1994.
Source: Masters Abstracts International, Volume: 45-06, page: 3173. Abstract precedes thesis as [2] preliminary leaves. Typescript. Includes bibliographical references (leaves 52-53).
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Rodgers, James David, and jdr@cgs vic edu au. "On E-Pseudovarieties of Finite Regular Semigroups." RMIT University. Mathematical and Geospatial Sciences, 2007. http://adt.lib.rmit.edu.au/adt/public/adt-VIT20080808.155720.

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An e-pseudovariety is a class of finite regular semigroups closed under the taking of homomorphic images, regular subsemigroups and finite direct products. Chapter One consists of a survey of those results from algebraic semigroup theory, universal algebra and lattice theory which are used in the following two chapters. In Chapter Two, a theory of generalised existence varieties is developed. A generalised existence variety is a class of regular semigroups closed under the taking of homomorphic images, regular subsemigroups, finite direct products and arbitrary powers. Equivalently, a generalised e-variety is the union of a directed family of existence varieties. It is demonstrated that a class of finite regular semigroups is an e-pseudovariety if and only if the class consists only of the finite members of some generalised existence variety. The relationship between certain lattices of e-pseudovarieties and generalised existence varieties is explored and a usefu l complete surjective lattice homomorphism is found. A study of complete congruences on lattices of existence varieties and e-pseudovarieties forms Chapter Three. In particular it is shown that a certain meet congruence, whose description is relatively simple, can be extended to yield a complete congruence on a lattice of e-pseudovarieties of finite regular semigroups. Ultimately, theorems describing the method of construction of all complete congruences of lattices of e-pseudovarieties whose members are finite E-solid or locally inverse regular semigroups are proved.
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Bourne, Thomas. "Counting subwords and other results related to the generalised star-height problem for regular languages." Thesis, University of St Andrews, 2017. http://hdl.handle.net/10023/12024.

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The Generalised Star-Height Problem is an open question in the field of formal language theory that concerns a measure of complexity on the class of regular languages; specifically, it asks whether or not there exists an algorithm to determine the generalised star-height of a given regular language. Rather surprisingly, it is not yet known whether there exists a regular language of generalised star-height greater than one. Motivated by a theorem of Thérien, we first take a combinatorial approach to the problem and consider the languages in which every word features a fixed contiguous subword an exact number of times. We show that these languages are all of generalised star-height zero. Similarly, we consider the languages in which every word features a fixed contiguous subword a prescribed number of times modulo a fixed number and show that these languages are all of generalised star-height at most one. Using these combinatorial results, we initiate work on identifying the generalised star-height of the languages that are recognised by finite semigroups. To do this, we establish the generalised star-height of languages recognised by Rees zero-matrix semigroups over nilpotent groups of classes zero and one before considering Rees zero-matrix semigroups over monogenic semigroups. Finally, we explore the generalised star-height of languages recognised by finite groups of a given order. We do this through the use of finite state automata and 'count arrows' to examine semidirect products of the form A x Zr where A is an abelian group and Zr is the cyclic group of order r.
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Pecuchet, Jean-Pierre. "Automates boustrophédons : langages reconnaissables de mots infinis et variétés de semigroupes." Rouen, 1986. http://www.theses.fr/1986ROUES005.

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La 1ère partie traite des automates boustrophédons, du semi-groupe de Birget et du monoïde inversif libre. La 2ème partie étudie le comportement infini d'un automate boustrophédon, la 3ème partie est consacrée aux variétés de semi-groupes et aux mots infinis. La 4ème partie poursuit la classification des langages rationnels de mots infinis à l'aide des variétés des semi-groupes
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Wang, Yanhui. "Beyond regular semigroups." Thesis, University of York, 2012. http://etheses.whiterose.ac.uk/2373/.

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The topic of this thesis is the class of weakly U-abundant semigroups. This class is very wide, containing inverse, orthodox, regular, ample, adequate, quasi-adequate, concordant, abundant, restriction, Ehresmann and weakly abundant semigroups. A semigroup $S$ with subset of idempotents U is weakly U-abundant if every $\art_U$-class and every $\elt_U$-class contains an idempotent of U, where $\art_U$ and $\elt_U$ are relations extending the well known Green's relations $\ar$ and $\el$. We assume throughout that our semigroups satisfy a condition known as the Congruence Condition (C). We take several approaches to weakly $U$-abundant semigroups. Our first results describe those that are analogous to completely simple semigroups. Together with an existing result of Ren this determines the structure of those weakly $U$-abundant semigroups that are analogues of completely regular semigroups, that is, they are superabundant. Our description is in terms of a semilattice of rectangular bands of monoids. The second strand is to aim for an extension of the Hall-Yamada theorem for orthodox semigroups as spined products of inverse semigroups and fundamental orthodox semigroups. To this end we consider weakly $B$-orthodox semigroups, where $B$ is a band. We note that if $B$ is a semilattice then a weakly $B$-orthodox semigroup is exactly an Ehresmann semigroup. We provide a description of a weakly $B$-orthodox semigroup $S$ as a spined product of a fundamental weakly $\overline{B}$-orthodox semigroup $S_B$ (depending only on $B$) and $S/\gamma_B$, where $\overline{B}$ is isomorphic to $B$ and $\gamma_B$ is the analogue of the least inverse congruence on an orthodox semigroup. This result is an analogue of the Hall-Yamada theorem for orthodox semigroups. In the case that $B$ is a normal band, or $S$ is weakly $B$-superabundant, we find a closed form $\delta_B$ for $\gamma_B$, which simplifies our result to a straightforward form. For the above to work smoothly in the case $S$ is weakly $B$-superabundant, we need to find a canonical fundamental weakly $B$-superabundant subsemigroup of $S_B$. This we do, and give the corresponding answers in the case of the Hall semigroup $W_B$ and a number of intervening semigroups. We then change our direction. A celebrated result of Nambooripad shows that regular semigroups are determined by ordered groupoids built over a regular biordered set. Our aim, achieved at the end of the thesis, is to extend Nambooripad's work to {\em weakly $U$-regular} semigroups, that is, weakly $U$-abundant semigroups with (C) and $U$ generating a regular subsemigroup whose set of idempotents is $U$. As an intervening step we consider weakly $B$-orthodox semigroups in this light. We take two approaches. The first is via a new construction of an inductive generalised category over a band. In doing so we produce a new approach to characterising orthodox semigroups, by using inductive generalised groupoids. We show that the category of weakly $B$-orthodox semigroups is isomorphic to the category of inductive generalised categories over bands. Our approach is influenced by that of Nambooripad, however, there are significant differences in strategy, the first being the introduction of generalised categories and the second being that it is more convenient to consider (generalised) categories equipped with pre-orders, rather than with partial orders. Our work may be regarded as extending a result of Lawson for Ehresmann semigroups. We also examine the trace of a weakly $B$-orthodox semigroup, which is a primitive weakly $B$-orthodox semigroup. We then take a more `traditional' approach to weakly $B$-orthodox semigroups via band categories and weakly orthodox categories over a band, equipped with two pre-orders. We show that the category of weakly $B$-orthodox semigroups is equivalent to the category of weakly orthodox categories over bands. To do so we must substantially adjust Armstrong's method for concordant semigroups. Finally, we consider the most general case of weakly $U$-regular semigroups. Following Nambooripad's theorem, which establishes a correspondence between algebraic structures (inverse semigroups) and ordered structures (inductive group-oids), we build a correspondence between the category of weakly $U$-regular semigroups and the category of weakly regular categories over regular biordered sets, equipped with two pre-orders.
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Smith, Paula Mary. "Orders in completely regular semigroups." Thesis, University of York, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.280477.

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Carey, Rachael Marie. "Graph automatic semigroups." Thesis, University of St Andrews, 2016. http://hdl.handle.net/10023/8645.

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In this thesis we examine properties and constructions of graph automatic semigroups, a generalisation of both automatic semigroups and finitely generated FA-presentable semigroups. We consider the properties of graph automatic semigroups, showing that they are independent of the choice of generating set, have decidable word problem, and that if we have a graph automatic structure for a semigroup then we can find one with uniqueness. Semigroup constructions and their effect on graph automaticity are considered. We show that finitely generated direct products, free products, finitely generated Rees matrix semigroup constructions, zero unions, and ordinal sums all preserve unary graph automaticity, and examine when the converse also holds. We also demonstrate situations where semidirect products, Bruck-Reilly extensions, and semilattice constructions preserve graph automaticity, and consider the conditions we may impose on such constructions in order to ensure that graph automaticity is preserved. Unary graph automatic semigroups, that is semigroups which have graph automatic structures over a single letter alphabet, are also examined. We consider the form of an automaton recognising multiplication by generators in such a semigroup, and use this to demonstrate various properties of unary graph automatic semigroups. We show that infinite periodic semigroups are not unary graph automatic, and show that we may always find a uniform set of normal forms for a unary graph automatic semigroup. We also determine some necessary conditions for a semigroup to be unary graph automatic, and use this to provide examples of semigroups which are not unary graph automatic. Finally we consider semigroup constructions for unary graph automatic semigroups. We show that the free product of two semigroups is unary graph automatic if and only if both semigroups are trivial; that direct products do not always preserve unary graph automaticity; and that Bruck-Reilly extensions are never unary graph automatic.
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Moreira, Joel Moreira. "Partition regular polynomial patterns in commutative semigroups." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1467131194.

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Books on the topic "Regular semigroup"

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Petrich, Mario. Completely regular semigroups. New York: Wiley, 1999.

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Pastijn, F. J. Regular semigroups as extensions. Boston: Pitman Advanced Pub. Program, 1985.

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Petrich, Mario, and Norman R. Reilly. Completely Regular Semigroups. Wiley & Sons, Incorporated, John, 2011.

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Regular Semigroups as Extensions (Research notes in mathematics). Longman Higher Education, 1986.

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Book chapters on the topic "Regular semigroup"

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Connes, Alain, Bernard de Wit, Antoine Van Proeyen, Sergey Gukov, Rafael Hernandez, Pablo Mora, Anatoli Klimyk, et al. "Completely Regular Semigroup." In Concise Encyclopedia of Supersymmetry, 97. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/1-4020-4522-0_120.

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Munn, W. D. "Semigroup Rings of Completely Regular Semigroups." In Lattices, Semigroups, and Universal Algebra, 191–201. Boston, MA: Springer US, 1990. http://dx.doi.org/10.1007/978-1-4899-2608-1_21.

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Pastijn, Francis J. "The Kernel of an Idempotent Separating Congruence on a Regular Semigroup." In Lattices, Semigroups, and Universal Algebra, 203–10. Boston, MA: Springer US, 1990. http://dx.doi.org/10.1007/978-1-4899-2608-1_22.

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Mordeson, John N., Davender S. Malik, and Nobuaki Kuroki. "Regular Semigroups." In Fuzzy Semigroups, 59–100. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-37125-0_3.

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Mordeson, John N., Davender S. Malik, and Nobuaki Kuroki. "Regular Fuzzy Expressions." In Fuzzy Semigroups, 291–301. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-37125-0_10.

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Reilly, Norman R. "Completely Regular Semigroups." In Lattices, Semigroups, and Universal Algebra, 225–42. Boston, MA: Springer US, 1990. http://dx.doi.org/10.1007/978-1-4899-2608-1_24.

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Alimpić, Branka P., and Dragica N. Krgović. "Some congruences on regular semigroups." In Lecture Notes in Mathematics, 1–10. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0083419.

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Romeo, P. G. "Biordered Sets and Regular Rings." In Semigroups, Algebras and Operator Theory, 81–87. New Delhi: Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2488-4_7.

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Nambooripad, K. S. S. "Regular Elements in von Neumann Algebras." In Semigroups, Algebras and Operator Theory, 39–45. New Delhi: Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2488-4_3.

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Brion, Michel, and Lex E. Renner. "Algebraic Semigroups Are Strongly π-Regular." In Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics, 55–59. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-0938-4_2.

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Conference papers on the topic "Regular semigroup"

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AUINGER, KARL. "ON EXISTENCE VARIETIES OF REGULAR SEMIGROUPS." In Semigroups, Algorithms, Automata and Languages. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812776884_0002.

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POLÁK, LIBOR. "OPERATORS ON CLASSES OF REGULAR LANGUAGES." In Semigroups, Algorithms, Automata and Languages. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812776884_0017.

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MITROVIĆ, MELANIJA, STOJAN BOGDANOVIĆ, and MIROSLAV ĆIRIĆ. "LOCALLY UNIFORMLY π-REGULAR SEMIGROUPS." In Proceedings of the International Conference. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792310_0009.

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STRAUBING, HOWARD. "FINITE SEMIGROUPS AND THE LOGICAL DESCRIPTION OF REGULAR LANGUAGES." In Semigroups, Algorithms, Automata and Languages. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812776884_0020.

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Xie, Xiang-Yun, and Jian Tang. "Fuzzy Regular Semigroups in Fuzzy Spaces." In 2009 International Workshop on Intelligent Systems and Applications. IEEE, 2009. http://dx.doi.org/10.1109/iwisa.2009.5072879.

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Wang, Lili, and Aifa Wang. "Some Properties of Regular Crypto - abundant Semigroups." In 3rd International Conference on Electric and Electronics. Paris, France: Atlantis Press, 2013. http://dx.doi.org/10.2991/eeic-13.2013.97.

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Liao, Zuhua, Shu Cao, Miaohan Hu, Yang Zhang, and Cuiyun Hao. "(epsilon, epsilon Vq (lamda, mu))-Fuzzy Regular * -Semigroups." In 2011 Fourth International Conference on Information and Computing (ICIC). IEEE, 2011. http://dx.doi.org/10.1109/icic.2011.3.

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Mora, W., and Y. Kemprasit. "Regular Elements of Generalized Order-Preserving Transformation Semigroups." In The International Conference on Algebra 2010 - Advances in Algebraic Structures. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814366311_0033.

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Tang, Gaohua, Huadong Su, and Yangjiang Wei. "Commutative rings and zero-divisor semigroups of regular polyhedrons." In 5th China–Japan–Korea International Ring Theory Conference. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812818331_0017.

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AFONIN, SERGEY, and ELENA KHAZOVA. "A NOTE ON FINITELY GENERATED SEMIGROUPS OF REGULAR LANGUAGES." In Proceedings of the International Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812708700_0001.

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