On rings asymptotically close to associative rings

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Abstract

The subject of this work is an extension of A. R. Kemer's results to a rather broad class of rings close to associative rings, over a field of characteristic 0 (in particular, this class includes the varieties generated by finite-dimensional alternative and Jordan rings). We prove the finite-basedness of systems of identities (the Specht property), the representability of finitely-generated relatively free algebras, and the rationality of their Hilbert series. For this purpose, we extend the Razymslov-Zubrilin theory to Kemer polynomials. For a rather broad class of varieties, we prove Shirshov's theorem on height.
Original languageAmerican English
Pages (from-to)227-267
JournalSiberian Advances in Mathematics
Volume17
Issue number4
StatePublished - 2007

Bibliographical note

Original Russian Text © A. Ya. Belov, 2007, published in Matematicheskie Trudy, 2007, Vol. 10, No. 1, pp. 29–96.

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