Separable algebra information

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

In field theory, a branch of algebra, an algebraic field extension E / F {\displaystyle E/F} is called a separable extension if for every α ∈ E {\displaystyle...

called the bidimension of A, measures the failure of separability. Let A be a finite-dimensional algebra over a field k. Then A is an Artinian ring. As A...

Neumann algebras are the direct integral of properly infinite factors. A von Neumann algebra that acts on a separable Hilbert space is called separable. Note...

field of S over K. An algebraic closure Kalg of K contains a unique separable extension Ksep of K containing all (algebraic) separable extensions of K within...

In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence { x n } n = 1 ∞ {\displaystyle...

automorphism of k. The separable closure of k is algebraically closed. Every reduced commutative k-algebra A is a separable algebra; i.e., A ⊗ k F {\displaystyle...

. It is well known that the CCR algebra is a simple (unless the sympletic form is degenerate) non-separable algebra and is unique up to isomorphism....

groups U(p, q); the field extension can be replaced by any degree 2 separable algebra, most notably a degree 2 extension of a finite field; generalizing...

Look up separable in Wiktionary, the free dictionary. Separability may refer to: Separable algebra, a generalization to associative algebras of the notion...

mathematics, a polynomial P(X) over a given field K is separable if its roots are distinct in an algebraic closure of K, that is, the number of distinct roots...

considerably simpler for algebras on separable spaces and most applications to other areas of mathematics or physics only use separable Hilbert spaces. Note...

Hopf algebra. The axioms are partly chosen so that the category of H-modules is a rigid monoidal category. The unit H-module is the separable algebra HL...

algebra Schur algebra Semisimple algebra Separable algebra Shuffle algebra Sigma-algebra Simple algebra Structurable algebra Supercommutative algebra...

In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with...

analysis, the Calkin algebra, named after John Williams Calkin, is the quotient of B(H), the ring of bounded linear operators on a separable infinite-dimensional...

In quantum mechanics, separable states are multipartite quantum states that can be written as a convex combination of product states. Product states are...

Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector...

example of a separable algebra extension since e = ∑ i = 1 n a i ⊗ B b i {\textstyle e=\sum _{i=1}^{n}a_{i}\otimes _{B}b_{i}} is a separability element satisfying...

extension Algebraic extension Splitting field Algebraically closed field Algebraic element Algebraic closure Separable extension Separable polynomial...

mathematics, a Galois extension is an algebraic field extension E/F that is normal and separable; or equivalently, E/F is algebraic, and the field fixed by the...

differential equation for the unknown f ( x ) {\displaystyle f(x)} will be separable if it can be written in the form d d x f ( x ) = g ( x ) h ( f ( x ) )...