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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The number of proper minimal quasivarieties of groupoids


Author: A. Shafaat
Journal: Proc. Amer. Math. Soc. 49 (1975), 54-58
MSC: Primary 08A15; Secondary 20L05
MathSciNet review: 0366783
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0366783-X
PII: S 0002-9939(1975)0366783-X
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



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