Equational theories of algebras with distributive congruences

Authors:
R. Padmanabhan and R. W. Quackenbush

Journal:
Proc. Amer. Math. Soc. **41** (1973), 373-377

MSC:
Primary 08A25

MathSciNet review:
0325498

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Abstract: If an equational class of algebras has the distributive or permutable congruence property then it is well known that it satisfies certain conditions, known as Mal'cev-type conditions. In this note such Mal'cev-type conditions are used to find minimal bases for certain equational theories of algebras. A typical result states that every finitely based equational theory of algebras with distributive and permutable congruences is one-based.

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1973-0325498-2

Keywords:
Equational classes of algebras,
equational theory,
distributive congruence property,
permutable congruence property,
Mal'cev-type conditions,
minimal bases

Article copyright:
© Copyright 1973
American Mathematical Society