commutative algebra noun2 •The branch of algebra concerned with commutative rings and objects related to them (such as ideals and modules).The subject of these notes is a part of commutative algebra, and is also closely related to certain topics in algebraic number theory and algebraic geometry. — 1992 •Any algebra (mathematical structure) in which the multiplication operation is commutative.The existence of commutative algebras of Toeplitz operators is not usual, for example there are not non trivial commutative algebras of Toeplitz operators acting on the Hardy space. — 2010 formscommutative algebras