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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 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
PII: S 0002-9939(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