Abstract
We consider the following question posted by Beidar and Mikhalev in 1995 for an associative ring [Formula: see text]: is it true that if the subrings [Formula: see text] and [Formula: see text] satisfy polynomial identities, then [Formula: see text] also satisfies a polynomial identity? Over a field of positive characteristic we establish new conditions on [Formula: see text] and [Formula: see text] that guarantee a positive answer to the question. We find upper and low bounds on the degrees of identities of [Formula: see text].
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