Topic
Bicyclic semigroup
About: Bicyclic semigroup is a research topic. Over the lifetime, 1507 publications have been published within this topic receiving 19311 citations.
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TL;DR: In this article, the translational hull of a semilattice of cancellative monoids (respectively a proper type-A semigroup, an E-reflexive type semigroup) is still the same type of semigroups.
10 citations
Journal Article•
TL;DR: In this article, the Betti numbers of the numerical semigroup ring K[T ] were studied when S is a 3-generated semigroup or telescopic. And they were studied for 4-generated symmetric semigroups and the so-called 4-irreducible numerical semigroup.
Abstract: For any numerical semigroup S, there are infinitely many numerical symmetric semigroups T such that S = T/2 (see below for the definition of T/2) is their half. We are studying the Betti numbers of the numerical semigroup ring K[T ] when S is a 3-generated numerical semigroup or telescopic. We also consider 4-generated symmetric semigroups and the so called 4-irreducible numerical semigroups.
10 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: The notion of m-irreducibility is introduced that extends the standard concept of irreducible of a numerical semigroup when the multiplicity is fixed and some properties of these numerical semigroups are given.
Abstract: In this paper we introduce the notion of m-irreducibility that extends the standard concept of irreducibility of a numerical semigroup when the multiplicity is fixed. We analyze the structure of the set of m-irreducible numerical semigroups, we give some properties of these numerical semigroups and we present algorithms to compute the decomposition of a numerical semigroup with multiplicity m into m-irreducible numerical semigroups.
10 citations
TL;DR: A natural extension of the usual definition of M-automata is considered which permits the automaton to utilise more of the structure of each monoid, and additionally allows it to be defined for S an arbitrary semigroup, and resulting automata are equivalent to the valence automata with rational target sets which arise in the theory of regulated rewriting systems.
10 citations