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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The number of proper minimal quasivarieties of groupoids
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by A. Shafaat PDF
Proc. Amer. Math. Soc. 49 (1975), 54-58 Request permission

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
  • P. M. Cohn, Universal algebra, Harper & Row, Publishers, New York-London, 1965. MR 0175948
  • 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
  • Shafaat Ahmad, On implicational completeness, Canadian J. Math. 26 (1974), 761–768. MR 349531, DOI 10.4153/CJM-1974-071-3
    • —, Unique factorization and Fermat’s last theorem in groupoidal domains (prepublication copy).
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 49 (1975), 54-58
  • MSC: Primary 08A15; Secondary 20L05
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0366783-X
  • MathSciNet review: 0366783