Showing papers on "Cancellative semigroup published in 1995"
51 citations
TL;DR: In this article, the existence of the bifree locally inverse semigroup BF L I (X) on a set X is proved by using canonical forms of the elements of the Bifree Completely Simple Semigroup BF C S (X).
18 citations
TL;DR: It is proved that every pair of families of subsets of an n-element set X is cancellative if every such pair satisfies AB gd, where τ = 2.3264.
Abstract: A pair ( A, B ) of families of subsets of an n-element set X is cancellative if, for all A, A′ ϵ A and B, B′ ϵ B, the following conditions hold: A⧹B = A′⧹B ⇒ A = A′ and B⧹A = B′⧹A ⇒ B = B′. We prove that every such pair satisfies AB \ gd , where τ = 2.3264. This is related to a conjecture of Erdo and Katona on cancellative families and to a conjecture of Simonyi on recovering pairs. For the latter, our result gives the best known upper bound.
18 citations
TL;DR: The weak closure of the image of the Weil representation of the infinite-dimensional symplectic group over a non-Archimedean field of an odd residue characteristic was described in this paper.
16 citations
TL;DR: It is shown that every semigroup pseudovarieties containing a group not in the subpseudovariety generated by all idempotent generated members of has no finite basis of pseudoidentities provided the five-element idem Potent generated 0-simple semigroup lies in .
Abstract: We show that every semigroup pseudovariety containing a group not in the subpseudovariety generated by all idempotent generated members of has no finite basis of pseudoidentities provided the five-element idempotent generated 0-simple semigroup lies in . This gives, in particular, a counterexample to a conjecture by J. Almeida.
15 citations
TL;DR: In this paper, it was shown that any regular semigroup is a homomorphic image of a regular semiigroup whose least full self-conjugate subsemigroup is unitary; the homomorphism is injective on the sub-semigroup.
12 citations
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TL;DR: In this article, a countable directed family of semigroup congruences is introduced, and a theory analogous to the theory of normal series for groups is developed, which is an effective tool for studying the structures of the lattices formed by certain species of semigroups.
Abstract: A countable directed family of semigroup congruences is introduced, and a theory analogous to the theory of normal series for groups is developed. This rather simple approach, surprisingly, is an effective tool for studying the structures of the lattices formed by certain species of semigroups (classes of semigroups closed under taking homomorphic images) such as varieties, pseudovarieties, and existence varieties etc.
10 citations
TL;DR: In this article, it was shown that the set of all 0-consistent ideals of an arbitrary semigroup with the zero forms a complete atomic Boolean algebra whose atoms are summands in the greatest orthogonal decomposition of this semigroup.
Abstract: The purpose of this paper is to prove that every semigroup with the zero is an orthogonal sum of orthogonal indecomposable semigroups. We prove that the set of all 0-consistent ideals of an arbitrary semigroup with the zero forms a complete atomic Boolean algebra whose atoms are summands in the greatest orthogonal decomposition of this semigroup.
9 citations
9 citations
8 citations
TL;DR: In this paper, the symmetric group and inverse semigroup onn symbols and a semigroup T⊂Cn is considered to be Sn-normal if α−1Tα ⊂T for every α∈Sn.
Abstract: IfSn andCn denote, respectively, the symmetric group and inverse semigroup onn symbols, thenSn⊂Cn and a semigroupT⊂Cn isSn-normal ifα−1Tα ⊂Tfor every α∈Sn. TheSn-normal semigroups are classified.
Journal Article•
TL;DR: In this paper, a simple proof of a known result is given: every inverse semigroup can be isomorphically embedded in the semigroup of cosets of a group, which is a semigroup that can be defined as a group of semigroups.
Abstract: In his seminal article of 1941, Paul Dubreil introduced \textit{complexes forts} of semigroups. Strong subsets of a semigroup $S$ form another semigroup under a natural multiplication. Properties of this semigroup are studied and some open problems raised (specially when $S$ is a group or an inverse semigroup). Also, a simple proof of a known result is given: every inverse semigroup can be isomorphically embedded in the semigroup of cosets of a group.
Journal Article•
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TL;DR: In this paper, the authors studied left A-ideals which are at the same time subsemigroups of semigroups and gave an outline of the extent to which this notion is useful.
Abstract: The aim of this paper is to study left A-ideals which are at th e same tim e semigroups, and to give an outline of th e extent to which this notion is useful. The notion has a ver y close relation to known notions such as quasi-z eros, mild-ideals, and directed groups. Th e re are also some connections with left-simple semigroups having no idempotents. The main result is a description of minimal semigroup left A-ideals in the commutative case. Left A-ideals appear in various areas of mathematics and unify several no tions. They are a generalization of left ideals in semigroups because any left ideal is at the same time a left A-ideal of a semigroup. We will deal with left A-ideals which are also subsemigroups of a given semigroup. In the theory of semigroups one question arises naturally: "Does there exist a minimal left A-ideal in the class of all left A-ideals which are at the same time subsemigroups of a given semigroup?" We give, in Theorem 12, a complete answer in the commutative case. The situation in the noncommutative case is discussed at the end of the paper. There exists also a ver y close relation to directed groups. First we briefl y recall some notions. DEFINITION 1. ((6)) A nonempt y subset GL of a semigroup S is called a left A-ideal of S (LA-ideal) if SGL H GL 7-= 0 for any s G S. A nonempty subset GR of a semigroup S is called a right A-ideal of S (RA-ideal) if GRS n GR 7^ 0 for any s G S. B y two-sided A-ideal, or simpl y A-ideal, we mean ct subset of S which is both a left and a right A-ideal of S.
01 Jan 1995
01 Jan 1995
TL;DR: For a topological semigroup S, Lawson constructed a semigroup (S) with the property that any local homomorphism dened in a neighborhood of the identity of S can be found in the neighborhood of S as discussed by the authors.
Abstract: For a topological semigroup S, Lawson constructed a semigroup ( S) with the property that any local homomorphism dened in a neighborhood of the identity of
TL;DR: In this paper, it was shown that if S is a semilattice of completely 0-simple semigroups and completely simple semiigroups, then the semigroup ring RS possesses an identity iff so does R(E(S)) for the subsemigroup of S generated by E(S).
Abstract: LetR be a ring with identity,S be a semigroup with the set of idempotentsE(S), and denote (E(S)) for the subsemigroup ofS generated byE(S). In this paper, we prove that ifS is a semilattice of completely 0-simple semigroups and completely simple semigroups, then the semigroup ringRS possesses an identity iff so doesR(E(S)); especially, the result is true forS being a completely regular semigroup.