On the quasivariety of BCK-algebras and its subvarieties
type: Item
instance of: scholarly article
title: On the quasivariety of BCK-algebras and its subvarieties
zbMATH Open document ID: 0818.06015
DOI: 10.1007/BF01190766
author: J. G. Raftery
author: W. J. Blok
published in: Algebra Universalis
publication date: 1995-02-22T00:00:00Z
review text: The quasivariety \({\mathcal B}{\mathcal C}{\mathcal K}\) of all BCK-algebras is the splitting quasivariety associated with a certain 3-element algebra \({\mathbf B}\) in a large variety \({\mathcal V}\), i.e. \({\mathcal B}{\mathcal C}{\mathcal K}\) consists of all algebras in \(\mathcal V\) that do not contain a subalgebra isomorphic to \({\mathbf B}\). Moreover, the varieties of BCK-algebras (i.e. varieties contained in \({\mathcal B}{\mathcal C}{\mathcal K})\) form a sublattice of the lattice of subquasivarieties of \({\mathcal B}{\mathcal C}{\mathcal K}\) and this sublattice contains a cofinal chain of order type \(\omega\), but no chain of quasicommutative BCK-varieties is cofinal among the varieties of BCK- algebras; neither arises a natural chain of varieties from Cornish's condition (J). Also some new examples of BCK-algebras are given.
Mathematics Subject Classification ID: 06F35
Mathematics Subject Classification ID: 08C15
Mathematics Subject Classification ID: 08B15
zbMATH DE Number: 724103
zbMATH Keywords: variety
zbMATH Keywords: tolerance
zbMATH Keywords: congruence
zbMATH Keywords: quasivariety
zbMATH Keywords: BCK-algebras
reviewed by: Wiesław A. Dudek
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 724103