Meaning of commutative algebra | Babel Free

Definitions

1. The branch of algebra concerned with commutative rings and objects related to them (such as ideals and modules).
   countable, uncountable
2. Any algebra (mathematical structure) in which the multiplication operation is commutative.
   countable, uncountable

Equivalents

Examples

“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.”

“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.”

“Theorem. If the complex of the linearly independent numbers of the form #92;zetaa-a#92;zeta be deleted from an algebra, the remaining numbers form a commutative algebra.”

“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.”

“We devote this chapter to the study of unitary commutative algebras in dg-modules, in simplicial modules and in cosimplicial modules.”

CEFR level