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

*Inna Mikhaylova*

#### Abstract

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.

Full Text: PDF