Topic
Cancellative semigroup
About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.
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TL;DR: A semilattice of simple poe -semigroups is defined in this article as an ordered semigroup having a greatest element, that is, an ordered order semigroup (:po -semigroup) having the greatest element.
Abstract: -semigroup -that is an ordered semigroup (:po -semigroup) having a greatest element - is a semilattice of simple semigroups if and only if it is a semilattice of simple poe -semigroups [3].
50 citations
TL;DR: In this article, the authors obtained important results on commutative Δ-semigroups, namely, they showed that Δ-Semigroups can be decomposed into commutativity-constrained semigroups.
Abstract: In this paper entitled on commutative Delta-Semigroups, we have obtained important results on commutative Δ-semigroups.
49 citations
01 Jan 1976
TL;DR: In this article, it was shown that almost all semigroups on n elements have the following property: the n elements are split into sets A, B and there is an e E Bsothatwheneverx,y E A,xy E B,butifxoryisinB,xy = e.
Abstract: The number of semigroups on n elements is counted asymptotically for large n. It is shown that "almost all" semigroups on n elements have the following property: The n elements are split into sets A, B and there isan e E Bsothatwheneverx,y E A,xy E B,butifxoryisinB,xy = e. 1. The problem. Fix a labelled n-element set [n] = (1, ... , n}. A semigroup SG on [n] is an associative binary operation (denoted by concatenation). Let S(n) denote the number of semigroups on [n]. We find an asymptotic approximation to S(n). Let (1.1) f(t) = ( )t+(n-t)2
48 citations
TL;DR: In this paper, the star representations on Hubert space of the inverse semigroup are studied, and specific examples of star representations are constructed for the /'-algebra of a number of the most important examples of inverse semigroups.
Abstract: In this paper the star representations on Hubert space of the /'-algebra of an inverse semigroup are studied. It is shown that the set of all irreducible star representations form a separating family for the /'-algebra. Then specific examples of star representations are constructed, and some theory of star representations is developed for the /'-algebra of a number of the most important examples of inverse semigroups. Introduction. Let 5 be a semigroup (as defined in [2, p.l]). If a, b E S, we write ab for the semigroup product of a with b. Let ll(S) be the set of all complex-valued functions fon S such that 11/11, = L l/(a)l<~. aGS lif.gE /'(S), then the convolution product / * g is given by the definition (f*gXc)= Z f(fl)s(b), cES. a,b with ab=c With convolution multiplication and norm II • II1, I1 (S) is a Banach algebra. If a E S, we identify a with the function which takes the value 1 at a and is 0 everywhere else. In this way S is embedded in /'(S). Having made this identification, when /G P(S) we have /= £ f(a)a. A map a —*■ a* of S into S is called an involution on S if (ab)* = b*a* all a, b E S, and (a*)* a all a G S. If S has an involution *, then P(S) has an involution * defined by the rule /* = E /(a)*«*, feHs), a£5 Received by the editors September 12, 1974. AMS (MOS) subject classifications (1970). Primary 43A65; Secondary 43A20.
48 citations
15 Jan 2003
TL;DR: In this article, it was shown that the automorphisms of the endomorphism semigroup of a free monoid or a free semigroup are either inner or mirror inner.
Abstract: We determine all isomorphisms between the endomorphism semigroups of free monoids or free semigroups and prove that automorphisms of the endomorphism semigroup of a free monoid or a free semigroup are inner or mirror inner. In particular, we answer a question of B. I. Plotkin.
48 citations