The Operator L n on Quasivarieties of Universal Algebras

Сибирский математический журнал

article

A. I. Budkin¹ 

[1] Altai State University

关键词: quasivariety;    variety;    universal algebra;    congruence-permutable variety;    Levi class;   

DOI  :  10.1134/S0037446619040025

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

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.

【 授权许可】

CC BY