FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2002, VOLUME 8, NUMBER 3, PAGES 829-876

On independently based varieties of monoids

V. Yu. Popov

Abstract

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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.

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