commutative algebra

1. (mathematics) The branch of algebra concerned with commutative rings and objects related to them (such as ideals and modules).
   • 1992, R. Keith Dennis, Claudio Pedrini, Michael R. Stein, editors, Algebraic K-theory, Commutative Algebra, and Algebraic Geometry: Proceedings of the Joint Seminar, American Mathematical Society:
   • 2003, Ragnar-Olaf Buchweitz, Morita contexts, idempotents, and Hochschild cohomology — with applications to invariant rings, Luchezar L. Avramov, Marcel Morales, Marc Chardin, Claudia Polini (editors), Commutative Algebra: Interactions with Algebraic Geometry: International Conference, American Mathematical Society, page 27 ↗,

     It is not until section 7 that we deal with commutative algebra proper, whereas the sections leading up to it should be seen as advocacy that excursions into noncommutative algebra can help to shed light on problems in commutative algebra.

2. (algebra) Any algebra (mathematical structure) in which the multiplication operation is commutative.

   Hyponym: polynomial ring

• (algebra which has a commutative multiplication operation) Abelian algebra

• noncommutative algebra concerned with rings that are not assumed to be commutative

• Italian: algebra commutativa
• Portuguese: álgebra comutativa
• Russian: коммутативная алгебра

• Italian: algebra commutativa
• Portuguese: álgebra comutativa
• Russian: коммутативная алгебра