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The Abelian Kernel of an Inverse Semigroup

Author

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  • A. Ballester-Bolinches

    (Departament de Matemàtiques, Universitat de València, Dr. Moliner 50, 46100 Burjassot, València, Spain)

  • V. Pérez-Calabuig

    (Departament de Matemàtiques, Universitat de València, Dr. Moliner 50, 46100 Burjassot, València, Spain)

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.

Suggested Citation

  • A. Ballester-Bolinches & V. Pérez-Calabuig, 2020. "The Abelian Kernel of an Inverse Semigroup," Mathematics, MDPI, vol. 8(8), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1219-:d:389162
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