Email this article The Operator Ln on Quasivarieties of Universal Algebras
- Authors: Budkin A.I.1
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Affiliations:
- Altai State University
- Issue: Vol 60, No 4 (2019)
- Pages: 565-571
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172479
- DOI: https://doi.org/10.1134/S0037446619040025
- ID: 172479
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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.
About the authors
A. I. Budkin
Altai State University
Author for correspondence.
Email: budkin@math.asu.ru
Russian Federation, Barnaul
