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Proceedings of the American Mathematical Society

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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?)

  • [1] P. M. Cohn, Universal algebra, Harper & Row, Publishers, New York-London, 1965. MR 0175948
  • [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
  • [4] -, Unique factorization and Fermat's last theorem in groupoidal domains (prepublication copy).

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0366783-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