commutative algebra

Definitions

1. 1

   The branch of algebra concerned with commutative rings and objects related to them (such…

   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.
2. 2

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

   • 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.

The neighborhood

• neighbornoncommutative algebra