Decidability of equational theories of coverings of semigroup varieties
V. Yu. Popov
Ural State University
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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Siberian Mathematical Journal, 2001, 42:6, 1132–1141
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
\paper Decidability of equational theories of coverings of semigroup varieties
\jour Sibirsk. Mat. Zh.
\jour Siberian Math. J.
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