Epigroups are semigroups equipped with an additional unary operation called pseudoinversion. Each finite semigroup can be considered as an epigroup. We prove the following theorem announced by Zhil'tsov in 2000: the equational theory of the class of all epigroups coincides with the equational theory of the class of all finite epigroups and is decidable. We show that the theory is not finitely based but provide a transparent infinite basis for it.

Source : oai:HAL:hal-01352849v1

Volume: Vol. 17 no. 3

Section: Combinatorics

Published on: June 7, 2016

Submitted on: September 11, 2013

Keywords: finite basis proble,epigroup, finite semigroup, decidability of equational theory,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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