The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Yang Hao-bo - One of the best experts on this subject based on the ideXlab platform.
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TWO NOTES OF MAXIMAL INVERSE SubsemigroupS OF FULL TRANSFORMATION SEMIGROUPS
Journal of Mathematics, 2004Co-Authors: Yang Hao-boAbstract:Let T_n be the full transformation semigroup on the set X_n={1,2,…,n}. In this paper we show that every maximal inverse Subsemigroup of T_n has a group kernel. We construct two new classes of maximal Subsemigroups of T_n from a group H-class and some subsemilattices of T_n, which are partial answers to the Schein’s problem of characterizing the maximal inverse Subsemigroups of T_n.
Pratyayananda Das - One of the best experts on this subject based on the ideXlab platform.
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Fuzzy regular and inverse Subsemigroups
Fuzzy Sets and Systems, 1997Co-Authors: Pratyayananda DasAbstract:Abstract Regular and inverse ( a , b ; e a , e a V q ( a , b ) ) — fuzzy Subsemigroups are defined. The concept of fuzzy analogue of normal Subsemigroup is introduced. Using a type of fuzzy congruence relation, a fuzzy quotient subgroup of a fuzzy inverse Subsemigroup is constructed. Some results concerning the interrelationship between fuzzy analogues of unitary Subsemigroup, inverse Subsemigroup and closed Subsemigroup of an inverse semigroup are obtained.
East James - One of the best experts on this subject based on the ideXlab platform.
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Computing finite semigroups
'Elsevier BV', 2019Co-Authors: East James, Egri-nagy Attila, Mitchell, James D., Peresse YannAbstract:Using a variant of Schreier's Theorem, and the theory of Green's relations, we show how to reduce the computation of an arbitrary Subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples of semigroups to which these results apply include many important classes: transformation semigroups, partial permutation semigroups and inverse semigroups, partition monoids, matrix semigroups, and Subsemigroups of finite regular Rees matrix and 0-matrix semigroups over groups. For any Subsemigroup of such a semigroup, it is possible to, among other things, efficiently compute its size and Green's relations, test membership, factorize elements over the generators, find the semigroup generated by the given Subsemigroup and any collection of additional elements, calculate the partial order of the D-classes, test regularity, and determine the idempotents. This is achieved by representing the given Subsemigroup without exhaustively enumerating its elements. It is also possible to compute the Green's classes of an element of such a Subsemigroup without determining the global structure of the semigroup.Peer reviewe
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Computing finite semigroups
'Elsevier BV', 2019Co-Authors: East James, Egri-nagy Attila, Mitchell, James D., Peresse YannAbstract:Using a variant of Schreier's Theorem, and the theory of Green's relations, we show how to reduce the computation of an arbitrary Subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples of semigroups to which these results apply include many important classes: transformation semigroups, partial permutation semigroups and inverse semigroups, partition monoids, matrix semigroups, and Subsemigroups of finite regular Rees matrix and 0-matrix semigroups over groups. For any Subsemigroup of such a semigroup, it is possible to, among other things, efficiently compute its size and Green's relations, test membership, factorize elements over the generators, find the semigroup generated by the given Subsemigroup and any collection of additional elements, calculate the partial order of the D-classes, test regularity, and determine the idempotents. This is achieved by representing the given Subsemigroup without exhaustively enumerating its elements. It is also possible to compute the Green's classes of an element of such a Subsemigroup without determining the global structure of the semigroup.PreprintPostprintPeer reviewe
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[In Press] Transformation representations of sandwich semigroups
U.S. Taylor and Francis, 2018Co-Authors: East JamesAbstract:Let a be an element of a semigroup S. The local Subsemigroup of S with respect to a is the Subsemigroup aSa of S. The variant of S with respect to a is the semigroup with underlying set S and operation ⋆a defined by x⋆ay = xay for x, y ∈ S. We show that the following classes contain precisely the same semigroups, up to isomorphism: all local Subsemigroups of all finite full transformation semigroups; and all variants of all finite full transformation semigroups. This result was discovered as a result of some experiments (and accidents) when working with the Semigroups package for GAP
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Transformation representations of sandwich semigroups
2018Co-Authors: East JamesAbstract:Let $a$ be an element of a semigroup $S$. The local Subsemigroup of $S$ with respect to $a$ is the Subsemigroup $aSa$ of $S$. The variant of $S$ with respect to $a$ is the semigroup with underlying set $S$ and operation $\star_a$ defined by $x\star_ay=xay$ for $x,y\in S$. We show that the following classes contain precisely the same semigroups, up to isomorphism: all local Subsemigroups of all finite full transformation semigroups; and all variants of all finite full transformation semigroups. This result was discovered as a result of some experiments (and accidents) when working with the Semigroups package for GAP.Comment: 6 pages, 1 figur
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Sandwich semigroups in locally small categories I : foundations
Switzerland Birkhaeuser Science, 2018Co-Authors: Dolinka Igor, East James, Durdev Ivana, Honyam Preeyanuch, Sangkhanan Kritsada, Sanwong Jintana, Sommanee WoracheadAbstract:Fix (not necessarily distinct) objects i and j of a locally small category S, and write Sij for the set of all morphisms i→ j. Fix a morphism a ∈ Sji, and define an operation ⋆ a on Sij by x⋆a y= xay for all x, y ∈ Sij. Then (Sij, ⋆a) is a semigroup, known as a sandwich semigroup, and denoted by Sija. This article develops a general theory of sandwich semigroups in locally small categories. We begin with structural issues such as regularity, Green’s relations and stability, focusing on the relationships between these properties on Sija and the whole category S. We then identify a natural condition on a, called sandwich regularity, under which the set Reg(Sija) of all regular elements of Sija is a Subsemigroup of Sija. Under this condition, we carefully analyse the structure of the semigroup Reg(Sija), relating it via pullback products to certain regular Subsemigroups of Sii and Sjj, and to a certain regular sandwich monoid defined on a subset of Sji; among other things, this allows us to also describe the idempotent-generated Subsemigroup E(Sija) of Sija. We also study combinatorial invariants such as the rank (minimal size of a generating set) of the semigroups Sija, Reg(Sija) and E(Sija); we give lower bounds for these ranks, and in the case of Reg(Sija) and E(Sija) show that the bounds are sharp under a certain condition we call MI-domination. Applications to concrete categories of transformations and partial transformations are given in Part II. NOTE: SOME OF THE SCIENTIC SYMBOLS CAN NOT BE REPRESENTED CORRECTLY IN THE ABSTRACT. PLEASE READ WITH CAUTION AND REFER TO THE ORIGINAL THESIS
Liu Wang-jin - One of the best experts on this subject based on the ideXlab platform.
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Fuzzy regular Subsemigroups in semigroups
Information Sciences, 1993Co-Authors: Wang Xue-ping, Liu Wang-jinAbstract:Abstract In this paper, we define the fuzzy regular Subsemigroups and fuzzy left (right, intra-) regular Subsemigroup in semigroups. Also, some properties of them are studied.
Alexander J. Ovsyannikov - One of the best experts on this subject based on the ideXlab platform.
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Inverse Semigroups with Certain Types of Lattices of Full Inverse Subsemigroups
Semigroups and Their Subsemigroup Lattices, 1996Co-Authors: Lev N. Shevrin, Alexander J. OvsyannikovAbstract:As we mentioned in the Preface, one can treat inverse semigroups as unary semi-groups, i.e. as algebraic systems with two operations: the binary operation of multiplication and the unary operation of taking the inverse element. From this point of view it is natural to associate with any inverse semigroup S the lattice of all subsystems, i.e. unary Subsemigroups of S. But a unary Subsemigroup of an inverse semigroup is none other than an inverse Subsemigroup. So we shall consider the lattice SubiS of all inverse Subsemigroups of S (of course, again the empty set is treated as an inverse Subsemigroup). In view of the identity (xy)−1 = y −1 x −1, which is valid in any inverse semigroup, the join of two inverse Subsemigroups of an inverse semigroup S is an inverse Subsemigroup; therefore SubiS is a sublattice of SubS. It is easy to see that SubS = SubiS if and only if S is a periodic Clifford semigroup. This observation will be used several times below without explicit reference. For an arbitrary group G, the lattice SubiG coincides with the lattice of all subgroups of G augmented by the adjoined zero. It follows that, in any general considerations of lattices of inverse Subsemigroups, the case when we deal with the subgroup lattice of a group is inevitably involved. As in the case of the usual Subsemigroup lattices, in examinations of lattices of all inverse Subsemigroups one succeeds not infrequently in realizing a reduction to groups.
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Semigroups and their Subsemigroup lattices
1996Co-Authors: Lev N. Shevrin, Alexander J. OvsyannikovAbstract:Preface. Part A: Semigroups with Certain Types of Subsemigroup Lattices. I. Preliminaries. II. Semigroups with Modular or Semimodular Subsemigroup Lattices. III. Semigroups with Complementable Subsemigroups. IV. Finiteness Conditions. V. Inverse Semigroups with Certain Types of Lattices of Inverse Subsemigroups. VI. Inverse Semigroups with Certain Types of Lattices of Full Inverse Subsemigroups. Part B: Properties of Subsemigroup Lattices. VII. Lattice Characteristics of Classes of Semigroups. VIII. Embedding Lattices in Subsemigroup Lattices. Part C: Lattice Isomorphisms. IX. Preliminaries on Lattice Isomorphisms. X. Cancellative Semigroups. XI. Commutative Semigroups. XII. Semigroups Decomposable into Rectangular Bands. XIII. Semigroups Defined by Certain Presentations. XIV. Inverse Semigroups. Bibliography. Index. List of Notations. List of Subsections Containing Unsolved Problems or Open Questions.
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Semigroups with Modular or Semimodular Subsemigroup Lattices
Semigroups and Their Subsemigroup Lattices, 1996Co-Authors: Lev N. Shevrin, Alexander J. OvsyannikovAbstract:Restrictions imposed on Subsemigroup lattices may be of different kinds. One of the prevalent types of restrictions is that of a lattice satisfying a fixed system of identities, in particular, a fixed identity. Classical examples are presented by distributivity and modularity. Semigroups with distributive and modular Subsemigroup lattices were described in the beginning of investigations on lattice properties of semigroups (in the modular case it was done modulo groups). The similarity of the resulting descriptions (which differ in restrictions for maximal subgroups only) provoked a question about possible unification of these results. It turns out that such unification can be formulated in terms of an arbitrary modular variety of lattices (i.e. any variety consisting of modular lattices). This result is central in Section 6. (Note that this topic is continued later in the book; namely, Section 29 is devoted to considerations of semigroups whose Subsemigroup lattices belong to a non-trivial variety; see also II.2.) This result is based on the more general considerations of Section 5, where semigroups with semimodular Subsemigroup lattices are described (modulo groups). A very special case of distributivity is the property of being a chain. We call a semigroup whose Subsemigroups form a chain a chain semigroup. We close Section 6 with a description of chain semigroups.
