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Semisimple algebra

In ring theory, a branch of mathematics, a semisimple algebra is an associative Artinian algebra over a field which has trivial Jacobson radical (only the zero element of the algebra is in the Jacobson radical). If the algebra is finite-dimensional this is equivalent to saying that it can be expressed as a Cartesian product of simple subalgebras.

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Semisimple algebra

Nodes24
Edges23
Triples9
Avg. degree1.92
Density0.083333
Components1

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Semisimple algebra

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related to Classification · 6
Semisimple algebra → Any, Artin, Emil Artin, Joseph Wedderburn, This, Wedderburn
related to Characterization · 2
Semisimple algebra → Cartesian, Let
is a · 1
Semisimple algebra → associative Artinian algebra over a field which has trivial Jacobson radical

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displaystyle simple algebra semisimple product algebras ideal finite-dimensional cartesian nilpotent radical field ideals times rad operatorname therefore isomorphic zero element

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SubjectPredicateObjectConfidenceSrc
Semisimple algebrais aassociative Artinian algebra over a field which has trivial Jacobson radical0.90text
Semisimple algebrarelated to CharacterizationLet0.60section
Semisimple algebrarelated to CharacterizationCartesian0.60section
Semisimple algebrarelated to ClassificationJoseph Wedderburn0.60section
Semisimple algebrarelated to ClassificationAny0.60section
Semisimple algebrarelated to ClassificationThis0.60section
Semisimple algebrarelated to ClassificationEmil Artin0.60section
Semisimple algebrarelated to ClassificationWedderburn0.60section
Semisimple algebrarelated to ClassificationArtin0.60section

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