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A variety generated by a class K of BCK-algebras consists of BCK-algebras if and only if it satisfies a certain kind of identity, first discovered by Komori. A similar phenomenon is shown to hold more generally in a certain class of quasivarieties of logic that includes not only the class of BCK-algebras but also such classes as the quasivariety of biresiduation algebras and quasivarieties of algebras with an equivalence operation. We describe a set of identities (which we call Komori identities), and show that the variety generated by a class K of algebras in one of the quasivarieties considered is contained in the quasivariety if and only it it satisfies a Komori identity. We use the result to establish (i) that the subvarieties of any of the quasivarieties studied are congruence 3-permutable and (ii) that the varietal join of two subvarieties of any of the quasivarieties studied is contained in the quasivariety.
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Tom
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79--106
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Bibliografia
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bwmeta1.element.baztech-article-BUJ1-0010-0059