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Siberian Mathematical Journal

, Volume 60, Issue 4, pp 565–571 | Cite as

The Operator Ln on Quasivarieties of Universal Algebras

  • A. I. BudkinEmail author
Article
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Abstract

Let n be an arbitrary natural and let be a class of universal algebras. Denote by Ln() the class of algebras G such that, for every n-generated subalgebra A of G, the coset a/R (aA) modulo the least congruence R including A × A is an algebra in . We investigate the classes Ln(). In particular, we prove that if is a quasivariety then Ln() is a quasivariety. The analogous result is obtained for universally axiomatizable classes of algebras. We show also that if is a congruence-permutable variety of algebras then Ln() is a variety. We find a variety of semigroups such that L1() is not a variety.

Keywords

quasivariety variety universal algebra congruence-permutable variety Levi class 

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© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.Altai State UniversityBarnaulRussia

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