6533b834fe1ef96bd129ce0d

RESEARCH PRODUCT

The Abelian Kernel of an Inverse Semigroup

Adolfo Ballester-bolinchesV. Pérez-calabuig

subject

profinite topologiesPure mathematicsabelian kernelsSemigroupGeneral Mathematicslcsh:Mathematics010102 general mathematicsfinite semigroup010103 numerical & computational mathematicslcsh:QA1-93901 natural sciencesDecidabilityextension problemKernel (algebra)Inverse semigroupComputer Science (miscellaneous)0101 mathematicsAbelian groupVariety (universal algebra)Element (category theory)partial automorphismsEngineering (miscellaneous)Mathematics

description

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.

yearjournalcountryeditionlanguage
2020-07-24Mathematics
10.3390/math8081219http://dx.doi.org/10.3390/math8081219