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Sib. J. Pure and Appl. Math., 2018, Volume 18, Issue 3, Pages 20–26 (Mi vngu475)  

On unsolvable $Q$-theories of ring varieties

A. I. Budkin

Altai State University, Barnaul

Abstract: Let $\mathcal{M}$ be any proper variety of associative rings. We prove that there exists an infinite set of varieties of associative rings containing $\mathcal{M}$ with unsolvable $Q$-theories. In particular, this result is a positive solution to the Mal'cev problem from the Kourovka Notebook on the existence of such varieties.

Keywords: quasivariety, variety, $Q$-theory, solvability, universal algebra, ring, Lee ring.

DOI: https://doi.org/10.33048/pam.2018.18.302

Full text: PDF file (119 kB)
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UDC: 510.53 512.55
Received: 28.04.2018

Citation: A. I. Budkin, “On unsolvable $Q$-theories of ring varieties”, Sib. J. Pure and Appl. Math., 18:3 (2018), 20–26

Citation in format AMSBIB
\Bibitem{Bud18}
\by A.~I.~Budkin
\paper On unsolvable $Q$-theories of ring varieties
\jour Sib. J. Pure and Appl. Math.
\yr 2018
\vol 18
\issue 3
\pages 20--26
\mathnet{http://mi.mathnet.ru/vngu475}
\crossref{https://doi.org/10.33048/pam.2018.18.302}


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