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 Sibirsk. Mat. Zh., 2001, Volume 42, Number 6, Pages 1361–1374 (Mi smj1393)

Decidability of equational theories of coverings of semigroup varieties

V. Yu. Popov

Ural State University

Abstract: For every proper semigroup variety $\mathfrak X$, there exists a semigroup variety $\mathfrak Y$ satisfying the following three conditions: (1) $\mathfrak Y$ covers $\mathfrak X$, (2) $\mathfrak X$ is finitely based then so is $\mathfrak Y$, and (3) the equational theory of $\mathfrak X$ is decidable if and only if so is the equational theory of $\mathfrak Y$. If $\mathfrak X$ is an arbitrary semigroup variety defined by identities depending on finitely many variables and such that all periodic groups of $\mathfrak X$ are locally finite, then one of the following two conditions holds: (1) all nilsemigroups of $\mathfrak X$ are locally finite and (2) $\mathfrak X$ includes a subvariety $\mathfrak Y$ whose equational theory is undecidable and which has infinitely many covering varieties with undecidable equational theories.

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English version:
Siberian Mathematical Journal, 2001, 42:6, 1132–1141

Bibliographic databases:

UDC: 512:519.4

Citation: V. Yu. Popov, “Decidability of equational theories of coverings of semigroup varieties”, Sibirsk. Mat. Zh., 42:6 (2001), 1361–1374; Siberian Math. J., 42:6 (2001), 1132–1141

Citation in format AMSBIB
\Bibitem{Pop01} \by V.~Yu.~Popov \paper Decidability of equational theories of coverings of semigroup varieties \jour Sibirsk. Mat. Zh. \yr 2001 \vol 42 \issue 6 \pages 1361--1374 \mathnet{http://mi.mathnet.ru/smj1393} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1876822} \zmath{https://zbmath.org/?q=an:0993.20037} \transl \jour Siberian Math. J. \yr 2001 \vol 42 \issue 6 \pages 1132--1141 \crossref{https://doi.org/10.1023/A:1012852812704} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000172981200012}