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arXiv · 1310.5023

A proof of Zhil'tsov's theorem on decidability of equational theory of epigroups

Inna Mikhailova
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Abstract

Epigroups are semigroups equipped with an additional unary operation called pseudoinversion. Each finite semigroup can be considered as 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.

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Inna Mikhailova. 2013-10-18. A proof of Zhil'tsov's theorem on decidability of equational theory of epigroups. https://arxiv.org/abs/1310.5023

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