On independently based varieties of monoids

V. Yu. Popov

Ural State Technical University

Abstract: There exists finitely based variety of monoids $\mathfrak Z$ such that there is no algorithm to decide, given a recursive system $\Sigma$ of semigroup identities, whether the variety of monoids given by the system $\Sigma$ in $\mathfrak Z$ is an independently based variety. There is no algorithm to decide, given an infinite recursive system $\Sigma$ of semigroup identities, whether the variety of monoids defined by the system $\Sigma$ is a finitely based variety.

UDC: 512:519.4

Received: 01.10.1999

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