central simple algebra
Let be a field. A central simple algebra (over ) is an algebra over , which is finite dimensional as a vector space over , such that
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has an identity element, as a ring
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is central: the center of equals (for all , we have for all if and only if )
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is simple: for any two sided ideal of , either or
By a theorem of Brauer, for every central simple algebra over , there exists a unique (up to isomorphism) division ring containing and a unique natural number such that is isomorphic to the ring of matrices with coefficients in .
Title | central simple algebra |
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Canonical name | CentralSimpleAlgebra |
Date of creation | 2013-03-22 11:49:08 |
Last modified on | 2013-03-22 11:49:08 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 7 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 16D60 |
Classification | msc 70K75 |