In mathematics, a separable algebra is a kind of semisimple algebra. It is a generalization to associative algebras of the notion of a separable field ...

30 мая 2023 г. · The concept of separable algebras is a strengthening of the concept of semisimple algebras, and a generalization of the concept of separable field extensions.

They are called separable. Examples of separable algebras are, on the one hand, central simple algebras, and on the other, separable fields. It turns out that a ...

]. • A localization of a separable algebra is separable. In particular, a pure transcendental extension K(Xi) (in any number of indetermi- nates) is separable.

The tensor product of two separable algebras is a separable algebra. Separability is transitive: if A is separable over S, and. S is separable over R, then A ...

11 июн. 2020 г. · Over a non-closed field, it is a common strategy to use separable algebras as invariants to distinguish algebraic and geometric objects.

1 мая 2017 г. · Definition 1 [Matsumura, Commutative Algebra, 1980, (27.D) + (27.G)]: A is separable over k if for all field extensions L of k, A⊗kL is reduced. Classification of separable algebras over a commutative ring why separable algebra is a generalisation of separable field ... how to split a separable algebra? - Mathematics Stack Exchange Другие результаты с сайта math.stackexchange.com

Abstract. Separable field extensions are essentially known since the 19th century and their formal definition was given by Ernst Steinitz in 1910.

29 нояб. 2014 г. · An algebra that is separable over its centre is called an Azumaya algebra. These algebras are important in the theory of the Brauer group of a ...

29,99 $ Separable Algebras over Commutative Rings. Download book PDF. Overview. Part of the book series: Lecture Notes in Mathematics (LNM, volume 181).