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...

{F}}).} A separable σ {\displaystyle \sigma } -algebra (or separable σ {\displaystyle \sigma } -field) is a σ {\displaystyle \sigma } -algebra F {\displaystyle...

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...

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...

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

For a commutative C*-algebra, A ^ ≅ Prim ⁡ ( A ) . {\displaystyle {\hat {A}}\cong \operatorname {Prim} (A).} Let H be a separable infinite-dimensional...

classification is possible, for separable simple nuclear C*-algebras. We begin with the abstract characterization of C*-algebras given in the 1943 paper by...

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...

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...

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...

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...

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...

commutative algebra, an étale algebra over a field is a special type of algebra, one that is isomorphic to a finite product of finite separable field extensions...

. 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....

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...

associative algebra over the field K {\displaystyle K} with Jacobson radical J {\displaystyle J} . Then A / J {\displaystyle A/J} is separable if and only...

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

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...

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...

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

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...

generalizes the notion of Euclidean space. It extends the methods of linear algebra and calculus from the two-dimensional Euclidean plane and three-dimensional...

In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns. This corresponds to the maximal...

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

exponential function exp : F → F×). For fields that are not algebraically closed (or not separably closed), the absolute Galois group Gal(F) is fundamentally...

for all vector spaces, and to avoid ambiguity may also be called the algebraic dual space. When defined for a topological vector space, there is a subspace...

Borel sets on X forms a σ-algebra, known as the Borel algebra or Borel σ-algebra. The Borel algebra on X is the smallest σ-algebra containing all open sets...

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

In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties...

If A is a separable C*-algebra, the weak-* topology is metrizable on bounded subsets. Thus the spectrum of a separable commutative C*-algebra A can be...