In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.

In mathematics, dimension theory is a branch of commutative algebra studying the notion of the dimension of a commutative ring, and by extension that of a scheme.

In commutative algebra, the constructible topology on the spectrum formula_1 of a commutative ring formula_2 is a topology where each closed set is the image of formula_3 in formula_1 for some algebra B over A .

Commutative diagrams play the role in category theory that equations play in algebra (see Barr Wells, Section 1.7).