Equational theories with a minority polynomial

Authors:
R. Padmanabhan and B. Wolk

Journal:
Proc. Amer. Math. Soc. **83** (1981), 238-242

MSC:
Primary 08B05; Secondary 20M05

DOI:
https://doi.org/10.1090/S0002-9939-1981-0624905-X

MathSciNet review:
624905

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Abstract: It is known that every finitely based variety of algebras with distributive and permutable congruences is one-based and those admitting a majority polynomial are two-based. In this note we prove two results, one similar to the above and the other in a completely opposite direction: (i) every finitely based variety of algebras of type satisfying the two-thirds minority condition is one-based and (ii) for every natural number , there exists a variety of algebras admitting even a full minority polynomial which is -based but not -based. An application to the strict consistency of defining relations for semigroups is given.

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DOI:
https://doi.org/10.1090/S0002-9939-1981-0624905-X

Article copyright:
© Copyright 1981
American Mathematical Society