commutative algebra

== English == === Noun === commutative algebra (countable and uncountable, plural commutative algebras) (mathematics) The branch of algebra concerned with commutative rings and objects related to them (such as ideals and modules). 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. (algebra) Any algebra (mathematical structure) in which the multiplication operation is commutative. Hyponym: polynomial ring ==== Synonyms ==== (algebra which has a commutative multiplication operation): Abelian algebra ==== Related terms ==== noncommutative algebra (concerned with rings that are not assumed to be commutative) ==== Translations ==== === Further reading === Associative algebra on Wikipedia.Wikipedia Glossary of commutative algebra on Wikipedia.Wikipedia List of commutative algebra topics on Wikipedia.Wikipedia Commutative algebra on Encyclopedia of Mathematics Commutative Algebra on Wolfram MathWorld