Congruence-permutable algebra
In universal algebra, two congruences are said to be permutable if . A congruence-permutable algebra is one in which all congruences are permutable. A variety of algebras is congruence-permutable if every algebra in the variety is congruence-permutable.
A Mal'cev term is a term M for which
A congruence-permutable variety is one whose signature contains a Mal'cev term.
Most classical varieties in abstract algebra, such as groups, rings, and Lie algebras, are congruence-permutable. Any variety that contains a group operation is congruence-permutable, and the Mal'cev term is .
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