Local finite basis property and local representability for varieties of associative rings

What is it about?

The author announces several important structural and algorithmic results in the theory of PI-rings. In particular, he claims that there exists an algorithm that, given a polynomial identity $f=0$ in algebras over an arbitrary Noetherian associative-commutative ring and a finite set $\Sigma$ of such identities, decides whether or not $f=0$ is a consequence of $\Sigma$. Proofs are just outlined. A detailed account of the results announced here appeared in the author's paper [Izv. Ross. Akad. Nauk Ser. Mat. 74 (2010), no. 1, 3–134;

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