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What is dimension of $Z(R)$ as a $k$ vector space?

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#abstract-algebra #ring-theory #field-theory #finite-fields #semi-simple-rings
465
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module over matrix ring

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#abstract-algebra #matrices #ring-theory #modules #semi-simple-rings
214
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Artin-Wedderburn: Decomposition of a semisimple Dual Hopf algebra

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#abstract-algebra #ring-theory #representation-theory #hopf-algebras #semi-simple-rings
133
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Concept and decomposition of semisimple rings

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#abstract-algebra #modules #representation-theory #semi-simple-rings
88
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We have $\pi(R) = \operatorname{End}_\mathbb{C}(V)$ is simple?

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#abstract-algebra #ring-theory #modules #representation-theory #semi-simple-rings
344
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Is a $R \otimes S$-module of the form $V \otimes W$ with $V$ simple $R$-module and $W$ simple $S$-module a simple module?

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#abstract-algebra #ring-theory #modules #representation-theory #semi-simple-rings
206
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A semisimple ring has only finitely many isomorphism classes of simple modules

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#abstract-algebra #modules #semi-simple-rings
280
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Why does the set of submodules of a module that are direct sums of irreducible submodules have a maximal element?

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#abstract-algebra #modules #noncommutative-algebra #semi-simple-rings
488
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If A is semisimple algebra then every A-module is completely reducible

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#ring-theory #semisimple-lie-algebras #semi-simple-rings
82
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A simple module isomorphism in Wedderburn theory

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#abstract-algebra #ring-theory #modules #noncommutative-algebra #semi-simple-rings
105
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R is not Artinian but R/J is semisimple

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#ring-theory #semi-simple-rings
73
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Jacobson Radical of integer matrices

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#matrices #ring-theory #semi-simple-rings
139
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Let V be an infinite dimensional vector space over a division ring D. The Set F={θ:V→V: Im(θ) is a finite dimensional subspace of V} is a simple ring.

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#abstract-algebra #vector-spaces #ideals #semi-simple-rings #division-ring
445
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A simple ring which is not semisimple

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#abstract-algebra #noncommutative-algebra #semi-simple-rings
499
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Semi-simple rings and fields.

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#ring-theory #commutative-algebra #field-theory #maximal-and-prime-ideals #semi-simple-rings

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