Geodesic
A proof of Zhil'tsov's theorem on decidability of equational theory of epigroups
Discrete mathematics & theoretical computer science, Tome 17 (2015-2016) no. 3.

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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. 
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     author = {Mikhaylova, Inna},
     title = {A proof of {Zhil'tsov's} theorem on decidability of equational theory of epigroups},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2015-2016},
     doi = {10.46298/dmtcs.2155},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2155/}
}
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Mikhaylova, Inna. A proof of Zhil'tsov's theorem on decidability of equational theory of epigroups. Discrete mathematics & theoretical computer science, Tome 17 (2015-2016) no. 3. doi : 10.46298/dmtcs.2155. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2155/

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