The Operator Ln on Quasivarieties of Universal Algebras

被引：0
作者：
A. I. Budkin
机构：
[1] Altai State University,
来源：
Siberian Mathematical Journal | 2019年 / 60卷
关键词：
quasivariety; variety; universal algebra; congruence-permutable variety; Levi class;
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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.
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页码：565 / 571
页数：6
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