Archivo de la etiqueta: finite semigroup

Paper «The abelian kernel of an inverse semigroup» published in Mathematics

Posted on por

The following paper has been published:
El siguiente artículo ha sido publicado:
El següent article ha sigut publicat:

Adolfo Ballester-Bolinches, Vicent Pérez-Calabuig.
The abelian kernel of an inverse semigroup.
Mathematics, 8(8):1219 (12 pages), 2020.

doi:10.3390/math8081219

Abstract

The problem of computing the abelian kernel of a finite semigroup was first solved by Delgado describing an algorithm that decides whether a given element of a finite semigroup S belongs to the abelian kernel. Steinberg extended the result for any variety of abelian groups with decidable membership. In this paper, we used a completely different approach to complete these results by giving an exact description of the abelian kernel of an inverse semigroup. An abelian group that gives this abelian kernel was also constructed.

2020 Mathematics Subject Classification: 20M10, 20M17

Keywords: finite semigroup; abelian kernels; profinite topologies; partial automorphisms; extension problem

Paper «An elementary proof of a theorem of Graham on finite semigroups» published in Mathematics

Posted on por

The following paper has been published:
El siguiente artículo ha sido publicado:
El següent article ha sigut publicat:

Adolfo Ballester-Bolinches and Vicent Pérez-Calabuig
An elementary proof of a theorem of Graham on finite semigroups.
Mathematics, 8(1):105 (5 pages), 2020.

doi:10.3390/math8010105

Abstract

The purpose of this note is to give a very elementary proof of a theorem of Graham that provides a structural description of finite 0-simple semigroups and its idempotent-generated subsemigroups.

2010 Mathematics Subject Classification: 20M10, 20M17

Keywords: finite semigroup; regular semigroup; 0-simple semigroup

Book chapter «On kernels of finite semigroups» published in Quad. Mat.

Posted on por

The following book chapter has been published:
El siguiente capítulo de libro ha sido publicado:
El capítol de llibre següent ha sigut publicat:

A. Ballester-Bolinches, V. Pérez-Calabuig.
On kernels of finite semigroups.
Overlapping of mathematics and humanities, 221-239, Quad. Mat., 20, Aracne, Rome, 2017.

ISBN 978-88-255-0237-4

Abstract:

A reduction theorem for the computability of the kernel of a finite semigroup associated to a variety of finite groups is presented in this survey article. This result turns out to be crucial in the proof of the computability of the prosoluble closure of a finitely generated subgroup of a free group.

2020 Mathematics Subject Classification: 20-02, 20M07.