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, it was shown that a finitely generated conical refinement monoid can be represented as a graph monoid by the behavior of the structural maps of the associated I-system at the free primes of the monoid.
12 citations
12 citations
TL;DR: In this paper, it was shown that a 2-testable monoid is either inherently non-finitely based or hereditarily finitely based, depending on whether or not the variety generated by the semigroup S contains the Brandt semigroup of order five.
Abstract: A monoid S
1 obtained by adjoining a unit element to a 2-testable semigroup S is said to be 2-testable. It is shown that a 2-testable monoid S
1 is either inherently non-finitely based or hereditarily finitely based, depending on whether or not the variety generated by the semigroup S contains the Brandt semigroup of order five. Consequently, it is decidable in quadratic time if a finite 2-testable monoid is finitely based.
12 citations
TL;DR: It was shown in this paper that every finite inverse semigroup having only solvable subgroups has no finite basis of identities, unless it is a strict inverse semi-convex semigroup.
Abstract: It is shown that every finite inverse semigroup having only solvable subgroups,viewed as a semigroup with the additional unary operation of inversion, has nofinite basis of identities, unless it is a strict inverse semigroup.
12 citations
TL;DR: In this paper, it was shown that a -simple strongly projective semigroup can be expressed by a Rees matrix semigroup over a left cancellative monoid and conversely, the result generalizes the classical theorem of Rees and amplifies the Rees theorem in semigroup given by Lallement and Petrich in 1969.
Abstract: A semigroup S is called rpp if all right principal ideals of S, regarded as S1-systems, are projective. An rpp semigroup S is said to be strongly rpp if for any a ∈ S, there exists a unique idempotent e such that and a = ea. In this paper, we show that a -simple strongly rpp semigroup can be expressed by a Rees matrix semigroup over a left cancellative monoid and conversely. Our result generalizes the classical theorem of Rees in 1940 and also amplifies the Rees theorem in semigroup given by Lallement and Petrich in 1969.
12 citations