commutative algebra

plural commutative algebras

1. countableuncountablemathematicsThe 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, Cornelius Greither, Cyclic Galois Extensions of Commutative Rings, Springer, page vii

   1 more example

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

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

   2017, Benoit Fresse, Homotopy of Operads and Grothendieck-Teichmuller Groups: Part 2, American Mathematical Society, page 163

   2 more examples

   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.

   1907, James Byrnie Shaw, Synopsis of Linear Associative Algebra, Carnegie Institution of Washington, page 46

   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, M. Loaiza, A. Sánchez-Numgaray, “On C*-Algebras of Super Toeplitz Operators with Radial Symbols”, in Roland V. Duduchava, Israel Gohberg, Sergei M. Grudsky, Vladimir Rabinovich, editors, Recent Trends in Toeplitz and Pseudodifferential Operators, Springer, page 175

   Synonyms: Abelian algebra