Abelian algebra

Summary

An abelian algebra is an algebra in which the commutator of the full congruence with itself is the trivial congruence. Equivalently, its term operations satisfy the term condition with equality. For groups this notion gives exactly the abelian groups, and modules over a ring are abelian algebras. Abelian algebras play the role of abelian groups in the general theory of solvable and nilpotent algebras.