Abstract
Let n be an arbitrary natural and let ℳ be a class of universal algebras. Denote by Ln(ℳ) the class of algebras G such that, for every n-generated subalgebra A of G, the coset a/R (a ∈ A) modulo the least congruence R including A × A is an algebra in ℳ. We investigate the classes Ln(ℳ). In particular, we prove that if ℳ is a quasivariety then Ln(ℳ) is a quasivariety. The analogous result is obtained for universally axiomatizable classes of algebras. We show also that if ℳ is a congruence-permutable variety of algebras then Ln(ℳ) is a variety. We find a variety ℘ of semigroups such that L1(℘) is not a variety.
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Russian Text © The Author(s), 2019, published in Sibirskii Matematicheskii Zhurnal, 2019, Vol. 60, No. 4, pp. 724–733.
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Budkin, A.I. The Operator Ln on Quasivarieties of Universal Algebras. Sib Math J 60, 565–571 (2019). https://doi.org/10.1134/S0037446619040025
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DOI: https://doi.org/10.1134/S0037446619040025