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).
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