Equational theories with a minority polynomial
Authors:
R. Padmanabhan and B. Wolk
Journal:
Proc. Amer. Math. Soc. 83 (1981), 238242
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 onebased and those admitting a majority polynomial are twobased. 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 twothirds minority condition is onebased 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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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002993919810624905X
PII:
S 00029939(1981)0624905X
Article copyright:
© Copyright 1981
American Mathematical Society
