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单词 CentralSimpleAlgebra
释义

central simple algebra


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

  • A has an identity elementMathworldPlanetmath, as a ring

  • A is central: the center of A equals K (for all zA, we have za=az for all aA if and only if zK)

  • A is simple: for any two sided ideal I of A, either I={0} or I=A

By a theoremMathworldPlanetmath of Brauer, for every central simple algebra A over K, there exists a unique (up to isomorphismMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath) division ring D containing K and a unique natural numberMathworldPlanetmath n such that A is isomorphic to the ring of n×n matrices with coefficients in D.

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更新时间:2025/5/4 1:02:26