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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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 $ \left\langle 3 \right\rangle $ satisfying the two-thirds minority condition is one-based and (ii) for every natural number $ n$, there exists a variety of algebras admitting even a full minority polynomial which is $ (n + 1)$-based but not $ n$-based. An application to the strict consistency of defining relations for semigroups is given.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0624905-X
PII: S 0002-9939(1981)0624905-X
Article copyright: © Copyright 1981 American Mathematical Society