List questions from semi-simple-rings

Published on 14 Mar 2019 - 0:43

193

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An infinite product of fields is not a semisimple ring

Published on 01 May 2019 - 21:06

63

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A certain decomposition of a semisimple Hopf algebra

Published on 13 May 2019 - 5:05

284

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Product of simple modules not semi-simple

Published on 16 Jun 2019 - 20:58

41

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Is the commutant of a semisimple algebra also semisimple?

Published on 08 Jul 2019 - 21:28

191

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Are zero rings and modules semisimple?

Published on 28 Jul 2019 - 22:39

194

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If R is a semisimple ring, then every simple R-module is isomorphic to a simple constituent of R

Published on 10 Sep 2019 - 6:37

124

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Why is $M_n(k)$ a semisimple $M_n(k)$-module?

Published on 15 Sep 2019 - 17:53

67

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When the permutation representation $k\Omega$ of a finite set $\Omega$ is semisimple, under the transitive action of a finite group.

Published on 16 Sep 2019 - 9:59

405

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Module is semisimple if and only if M is the sum of simple submodules.

Published on 28 Sep 2019 - 10:42

72

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Do these module theorems in algebra have a right version?

Published on 07 Oct 2019 - 16:35

172

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Is the following ring (artinian) semisimple? And are any of these attempts valid?

Published on 19 Nov 2019 - 19:40

26

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Is $R/J^2$ right finitely generated?

Published on 01 Mar 2020 - 8:26

496

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Semisimple quotient modules

Published on 04 Mar 2020 - 2:19

114

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Determinant polynomial of finite module over a semisimple algebra

Published on 05 Mar 2020 - 5:30

List Question

Group ring $R[G]$ semisimple if and only if $J = J^2$?

An infinite product of fields is not a semisimple ring

A certain decomposition of a semisimple Hopf algebra

Product of simple modules not semi-simple

Is the commutant of a semisimple algebra also semisimple?

Are zero rings and modules semisimple?

If R is a semisimple ring, then every simple R-module is isomorphic to a simple constituent of R

Why is $M_n(k)$ a semisimple $M_n(k)$-module?

When the permutation representation $k\Omega$ of a finite set $\Omega$ is semisimple, under the transitive action of a finite group.

Module is semisimple if and only if M is the sum of simple submodules.

Do these module theorems in algebra have a right version?

Is the following ring (artinian) semisimple? And are any of these attempts valid?

Is $R/J^2$ right finitely generated?

Semisimple quotient modules

Determinant polynomial of finite module over a semisimple algebra

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