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central simple algebra (Definition)

Let $ K$ be a field. A central simple algebra $ A$ (over $ K$) is an algebra $ A$ over $ K$, which is finite dimensional as a vector space over $ K$, such that

By a theorem of Brauer, for every central simple algebra $ A$ over $ K$, there exists a unique (up to isomorphism) division ring $ D$ containing $ K$ and a unique natural number $ n$ such that $ A$ is isomorphic to the ring of $ n \times n$ matrices with coefficients in $ D$.



"central simple algebra" is owned by djao.
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Cross-references: coefficients, matrices, isomorphic, natural number, division ring, ideal, simple, center, ring, identity element, vector space, finite dimensional, algebra, field
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This is version 2 of central simple algebra, born on 2001-10-19, modified 2002-02-13.
Object id is 363, canonical name is CentralSimpleAlgebra.
Accessed 6782 times total.

Classification:
AMS MSC16D60 (Associative rings and algebras :: Modules, bimodules and ideals :: Simple and semisimple modules, primitive rings and ideals)

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