Congruence-permutable algebra

In universal algebra, two congruences $\alpha, \beta$ are said to be permutable if $\alpha \circ \beta = \beta \circ \alpha$. 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

$M(x, x, y) = y = M(y, x, x).$

A congruence-permutable variety is one whose signature contains a Mal'cev term.