Equational theories of algebras with distributive congruences

Padmanabhan, R.; Quackenbush, R. W.

doi:10.1090/S0002-9939-1973-0325498-2

Equational theories of algebras with distributive congruences
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by R. Padmanabhan and R. W. Quackenbush PDF

Proc. Amer. Math. Soc. 41 (1973), 373-377 Request permission

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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