List questions from group-rings

Published on 15 Apr 2026 - 18:34

45

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Exponent of $1+J(GF),$ $J$ stands for Jacobson radical.

Published on 15 Apr 2026 - 21:52

231

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Group rings decomposition

Published on 30 Apr 2026 - 10:54

117

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Wedderburn decomposition of $F(Z_2\times Z_2).$

Published on 15 Apr 2026 - 8:57

407

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Group ring definition

Published on 14 Apr 2026 - 19:45

80

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Group algebra is domain iff doesn't contain nonzero element whose square is 0

Published on 17 Apr 2026 - 14:53

239

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

Published on 09 Apr 2026 - 8:10

87

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Extending scalars from $\mathbb{Z}[G]$ to $\mathbb{Q}[G]$

Published on 12 Apr 2026 - 12:38

133

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Group Algebra of a Discrete Group and Different Notions of a Group Algebra?

Published on 25 Mar 2026 - 6:06

165

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Decomposition of $C[G]$ as $C[G]$-module into direct sum of submodules of the form $Ce_{\chi}$

Published on 11 Apr 2026 - 13:58

28

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Showing W=ku+kv has a unique module structure over kG

Published on 13 Apr 2026 - 6:53

552

Views

Abstract proof that $\lvert H^2(G,A)\rvert$ counts group extensions.

Published on 25 Mar 2026 - 6:01

62

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trivial modules of group rings

Published on 10 Apr 2026 - 3:05

35

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Proving that $\mathbb{F}_p[x_1,\dots,x_n]/(x_1^p,\dots,x_n^p)$ is a complete intersection ring

Published on 25 Mar 2026 - 6:05

248

Views

Sums of Commutators in a Group Ring

Published on 11 Apr 2026 - 18:32

List Question

How orbits of $G$-sets and these characters are related

Exponent of $1+J(GF),$ $J$ stands for Jacobson radical.

Group rings decomposition

Wedderburn decomposition of $F(Z_2\times Z_2).$

Group ring definition

Group algebra is domain iff doesn't contain nonzero element whose square is 0

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

Extending scalars from $\mathbb{Z}[G]$ to $\mathbb{Q}[G]$

Group Algebra of a Discrete Group and Different Notions of a Group Algebra?

Decomposition of $C[G]$ as $C[G]$-module into direct sum of submodules of the form $Ce_{\chi}$

Showing W=ku+kv has a unique module structure over kG

Abstract proof that $\lvert H^2(G,A)\rvert$ counts group extensions.

trivial modules of group rings

Proving that $\mathbb{F}_p[x_1,\dots,x_n]/(x_1^p,\dots,x_n^p)$ is a complete intersection ring

Sums of Commutators in a Group Ring

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