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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

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