Geodesic
On unsolvable $Q$-theories of ring varieties
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 18 (2018) no. 3, pp. 20-26 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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A. I. Budkin. On unsolvable $Q$-theories of ring varieties. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 18 (2018) no. 3, pp. 20-26. http://geodesic.mathdoc.fr/item/VNGU_2018_18_3_a1/

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