Some fixed-point results on (generalized) Bruck-Reilly ∗-extensions of monoids

Eylem Guzel Karpuz,Ahmet Sinan Çevik,Jörg Koppitz,Ismail Naci Cangul

doi:10.1186/1687-1812-2013-78

Eylem Guzel Karpuz, Ahmet Sinan Çevik + Show 2 more

Open Access

https://doi.org/10.1186/1687-1812-2013-78

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Abstract

In this paper, we determine necessary and sufficient conditions for Bruck-Reilly and generalized Bruck-Reilly ∗-extensions of arbitrary monoids to be regular, coregular and strongly π-inverse. These semigroup classes have applications in various field of mathematics, such as matrix theory, discrete mathematics and p-adic analysis (especially in operator theory). In addition, while regularity and coregularity have so many applications in the meaning of boundaries (again in operator theory), inverse monoids and Bruck-Reilly extensions contain a mixture fixed-point results of algebra, topology and geometry within the purposes of this journal.MSC:20E22, 20M15, 20M18.

Highlights

Introduction and preliminariesIn combinatorial group and semigroup theory, for a finitely generated semigroup, a fundamental question is to find its presentation with respect to some system of generators and relators, and classify it with respect to semigroup classes
Many classes of regular semigroups are characterized by BruckReilly extensions; for instance, any bisimple regular w-semigroup is isomorphic to a Reilly extension of a group [ ] and any simple regular w-semigroup is isomorphic to a BruckReilly extension of a finite chain of groups [, ]
In [ ], the authors studied the structure theorem of the ∗-bisimple type A w -semigroups as the generalized Bruck-Reilly ∗-extension

Summary

Introduction

Introduction and preliminariesIn combinatorial group and semigroup theory, for a finitely generated semigroup (monoid), a fundamental question is to find its presentation with respect to some (irreducible) system of generators and relators, and classify it with respect to semigroup classes. In another important paper [ ], the author obtained a new monoid, namely the generalized Bruck-Reilly ∗-extension, and presented the structure of the ∗-bisimple type A w-semigroup. In [ ], the authors studied the structure theorem of the ∗-bisimple type A w -semigroups as the generalized Bruck-Reilly ∗-extension.

Results

Conclusion