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 paper, the authors give a complete characterization of when the (composite) semigroup ring is a generalized Krull domain and show that it is the case for all semigroup rings.
Abstract: In this article, we give a complete characterization of when the (composite) semigroup ring is a generalized Krull domain.
10 citations
TL;DR: In this paper, the authors studied algebraic structure of submeans on certain spaces of bounded real valued functions on a semigroup and found local conditions on these spaces in terms of submean for the existence of a left invariant mean.
Abstract: The purpose of this paper is to study some algebraic structure
of submeans on certain spaces $X$ of bounded real valued functions
on a semigroup and to find local conditions on $X$ in terms of submean
for the existence of a left invariant mean.
10 citations
01 Jan 2003
TL;DR: In this article, it is shown that two algebroid branches R and T are equivalent if and only if their Arf closures have the same value semigroup, which is an Arf numerical semigroup and can be expressed in terms of a finite set of information, a set of characters of the branch.
Abstract: Two algebroid branches are said to be equivalent if they have the same multiplicity sequence It is known that two algebroid branches R and T are equivalent if and only if their Arf closures, R and T ′ have the same value semigroup, which is an Arf numerical semigroup and can be expressed in terms of a finite set of information, a set of characters of the branch We extend the above equivalence to algebroid curves with d > 1 branches An equivalence class is described, in this more general context, by an Arf semigroup, that is not a numerical semigroup, but is a subsemigroup of N We express this semigroup in terms of a finite set of information, a set of characters of the curve, and apply this result to determine other curves equivalent to a given one AMS subject classification: 13H15, 14B05
10 citations
TL;DR: The boundary between the sub-logexponential and log-exponential monoids was studied in this article, where it was shown that a monoid M ∈ EDA is a regular sublog-exponentially monoid if and only if it is G nil ¯ ∩ EDA, the finite monoid in EDA having nilpotent subgroups.
10 citations
TL;DR: An abstract characterization of the inverse monoids that appear as monoids of bi-congruences of finite minimal algebras generating arithmetical varieties is provided and a matrix construction is introduced which might be of independent interest in inverse semigroup theory.
Abstract: This paper provides an abstract characterization of the inverse monoids that appear as monoids of bi-congruences of finite minimal algebras generating arithmetical varieties. As a tool, a matrix construction is introduced which might be of independent interest in inverse semigroup theory. Using this construction as well as Ramsey's theorem, we embed a certain kind of inverse monoid into a factorizable monoid of the same kind. As noticed by M. Lawson, this embedding entails that the embedded finite monoids have finite F-unitary cover.
10 citations