Permuting congruences

Summary

Two congruences on an algebra permute when their relational products in the two orders are equal. Then their join in the congruence lattice is simply their product, which makes it easy to compute. An algebra whose congruences all permute is called congruence-permutable; groups, rings and modules are examples. This property is the starting point of congruence-permutable varieties and of Mal'cev conditions.