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

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 t...

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Bibliographic Details
Published in:Discrete mathematics and theoretical computer science 2016-06, Vol.17 no. 3 (Combinatorics), p.179-202
Main Author: Mikhaylova, Inna
Format: Article
Language:English
Subjects:
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
Combinatorics
Computer Science
decidability of equational theory
Discrete Mathematics
epigroup
finite basis proble
finite semigroup
Theorems
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Summary: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.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.2155