On the number of the epimorphy skeletons of varieties
type: Item
instance of: scholarly article
title: On the number of the epimorphy skeletons of varieties
zbMATH Open document ID: 0854.08004
DOI: 10.1007/BF02104786
published in: Siberian Mathematical Journal
publication date: 1996-11-04T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 08B05
zbMATH DE Number: 916368
zbMATH Keywords: epimorphy skeleton
zbMATH Keywords: countable skeletons
zbMATH Keywords: number of pairwise nonisomorphic skeletons of varieties
zbMATH Keywords: finitely generated varieties
author: A. G. Pinus
MaRDI profile type: Publication
cites work: Q3997775
cites work: Algebras Whose Congruence Lattices are Distributive.
cites work: Joins and Direct Products of Equational Classes
full work available at URL: https://doi.org/10.1007/bf02104786
OpenAlex ID: W2046186571
description: scientific article; zbMATH DE number 916368