On the number of the epimorphy skeletons of varieties
In earlier work of the author [Algebra Logika 24, No. 5, 588-607 (1985; Zbl 0619.08005); Congruence-modular varieties of algebras (Russian) (1986; Zbl 0714.08003)] the notions of epimorphy skeleton and embeddability skeleton were introduced for an arbitrary variety of algebras. In a series of subsequent articles, the properties of skeletons were thoroughly studied for congruence-distributive varieties. The formulations of the properties were chiefly of universal character; i.e., the properties were valid for any nontrivial congruence-distributive variety of algebras. Essential distinctions were discovered only between countable skeletons of finitely generated varieties and those of varieties lacking this property. In this connection, a natural question arises about the number of pairwise nonisomorphic skeletons of varieties; here we assume that the signature of the varieties in question is at most countable. Differently generating varieties by finitely many pairwise nonisomorphic primal algebras, we can easily observe that there exists at least a countable number of congruence-distributive finitely generated varieties with nonisomorphic epimorphy skeletons. The purpose of the present article is to exhibit an example of a continuum of varieties whose epimorphy skeletons are pairwise nonisomorphic.
number of pairwise nonisomorphic skeletons of varieties
scientific article; zbMATH DE number 916368