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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11 citations
TL;DR: In this article, a bisimple left inverse semigroup S with identity element e as a quotient of the cartesian product Le×Re of the L-class Le of S and the R-class Re of S containing e is described.
Abstract: A semigroup S is called left inverse if every principal right ideal of S has a unique idempotent generator. We investigate D-classes of regular semigroups and of left inverse semigroups, characterizing those which are subsemigroups. We give a description of a bisimple left inverse semigroup S with identity element e as a quotient of the cartesian product Le×Re of the L-class Le of S and the R-class Re of S containing e. We also describe the maximal inverse semigroup homomorphic image of S.
11 citations
TL;DR: In this article, the translational hull of a type B semigroup is considered, and it is shown that it is itself a type semigroup, and some properties and characterizations of translational Hulls of such semigroups are given.
Abstract: In this paper, the translational hull of a type B semigroup is considered. We prove that the translational hull of a type B semigroup is itself a type B semigroup, and give some properties and characterizations of the translational hulls of such semigroups. Moreover, we consider the translational hulls of some special type B semigroups. These results strengthen the results of Fountain and Lawson (Semigroup Forum 32:79–86, 1985) on adequate semigroups. Finally, we give a new proof of a problem posted by Petrich on translational hulls of inverse semigroups in Petrich (Inverse Semigroups, Wiley, New York, 1984).
11 citations
TL;DR: In this paper, the authors studied strongly rpp-semigroups whose set of idempotents forms a right regular band and the relation is a congruence, and they gave a tighter description of the semilattice decomposition involving a system of connecting maps, which can always construct a right C-rpp semigroup by glueing up the given ingredients by the connecting maps.
Abstract: We study the strongly rpp-semigroups whose set of idempotents forms a right regular band and the relation ${\cal L}^* \vee {\cal R}$ is a congruence. This kind of strongly rpp-semigroups was called by Y.Q. Guo the right C-rpp semigroups and he characterized them as semilattice of direct products of left cancellative monoid with right zero semigroup. The aim of this paper is to improve upon Guo’s result, giving a tighter description of the semilattice decomposition involving a system of connecting maps. By using our result, we can always construct a right C-rpp semigroup by glueing up the given ingredients by the connecting maps. An example of an infinite right C-rpp semigroup is constructed.
11 citations
11 citations