The number of proper minimal quasivarieties of groupoids
Abstract: It is shown that if an algebra has more than one element, is freely generated in some variety by one element and has a cancellative endomorphism semigroup then it generates a minimal quasivariety. This is used to construct uncountably many minimal quasivarieties of groupoids that are not varieties.
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Keywords: Implicationally complete or minimal quasivarieties, (universal) algebras, groupoids, free monogenic groupoid, endomorphism semigroup, cancellative, identity, implication, proper quasivariety, fully invariant congruences, words
Article copyright: © Copyright 1975 American Mathematical Society