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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.

References [Enhancements On Off] (What's this?)

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  • [2] Jan Kalicki, The number of equationally complete classes of equations, Nederl. Akad. Wetensch. Proc. Ser. A. 58 = Indag. Math. 17 (1955), 660–662. MR 0074351
  • [3] Shafaat Ahmad, On implicational completeness, Canad. J. Math. 26 (1974), 761–768. MR 0349531
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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