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Coverings in epimorphy skeletons of varieties of algebras. (Russian) Zbl 0666.08004
In a previous paper [ibid. 24, No.5, 588-607 (1985; Zbl 0619.08005)] the author introduced and investigated the so-called isomorphism type. Let \({\mathcal M}\) be a variety of algebras, denote by \({\mathcal I}{\mathcal M}\) the set of all isomorphism types of all members of \({\mathcal M}\). Introduce the quasiorder \(\ll\) on \({\mathcal I}{\mathcal M}\) by rule: \(a\ll b\) iff for all algebras A, B of \({\mathcal M}\) of the isomorphism types a, b, A is a homomorphic image of B. The class (\({\mathcal I}{\mathcal M},\ll)\) is called the epimorphism skeleton. The paper contains solutions of some problems on the covering in epimorphism skeleton of \({\mathcal M}\), especially in the case of a congruence distributive variety \({\mathcal M}\).
Reviewer: I.Chajda

08B30 Injectives, projectives
08A35 Automorphisms and endomorphisms of algebraic structures
08B10 Congruence modularity, congruence distributivity
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