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Question about a group algebra being not Artinian

score 71 · Answer 1 · 2026-03-25 07:41:54

71

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Question about a group algebra being not Artinian

Published on 25 Mar 2026 - 7:41

score 155 · Answer 2 · 2026-03-25 07:46:02

155

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On minimal elements, w.r.t. inclusion, of non-empty subset of prime ideals of commutative rings

Published on 25 Mar 2026 - 7:46

score 135 · Answer 3 · 2026-03-25 09:28:31

135

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The finite generation of $M$, to conclude $M$ is Noetherian (when $R$ is Noetherian).

Published on 25 Mar 2026 - 9:28

score 229 · Answer 4 · 2026-03-25 07:41:48

229

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Consequence of epimorphism from Noetherian $R$-module

Published on 25 Mar 2026 - 7:41

score 1k · Answer 5 · 2026-04-13 22:08:41

1k

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If finite product of maximal ideals of ring $R$ is zero, then $R$ is Noetherian$\iff R$ is Artinian

Published on 13 Apr 2026 - 22:08

score 145 · Answer 6 · 2026-04-26 19:14:55

145

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Certain exact functor on the Grothendieck group of a module category

Published on 26 Apr 2026 - 19:14

score 149 · Answer 7 · 2026-03-25 07:49:28

149

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Noetherian module does not contain a submodule $N$ which is a direct sum of $n$ simple modules

Published on 25 Mar 2026 - 7:49

score 35 · Answer 8 · 2026-03-25 06:05:26

35

Views

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

score 1.5k · Answer 9 · 2026-04-15 07:17:15

1.5k

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Every Artinian ring is isomorphic to a direct product of Artinian local rings

Published on 15 Apr 2026 - 7:17

score 143 · Answer 10 · 2026-04-11 12:54:11

143

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Is the fiber product of local artinian rings again local artinian under these conditions?

Published on 11 Apr 2026 - 12:54

score 221 · Answer 11 · 2026-03-25 07:45:50

221

Views

If $V/F$ has basis $\{x_1,x_2,x_3,\dotsc\}$, $T'\colon V \to V$ is the right-shift operator, $W\subset V$ is $T'$-invariant, then $\dim V/W < \infty$?

Published on 25 Mar 2026 - 7:45

score 80 · Answer 12 · 2026-03-25 07:48:59

80

Views

Characterisation of Largest Semisimple Left Ideal

Published on 25 Mar 2026 - 7:48

score 113 · Answer 13 · 2026-04-09 06:18:47

113

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socle and essential extension of finitely generated mod over an artin algebra

Published on 09 Apr 2026 - 6:18

score 957 · Answer 14 · 2026-03-25 09:23:35

957

Views

Counterexample: Local Artinian ring is not a PID

Published on 25 Mar 2026 - 9:23

score 174 · Answer 15 · 2026-04-09 08:10:03

174

Views

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

Published on 09 Apr 2026 - 8:10

List Question

Question about a group algebra being not Artinian

On minimal elements, w.r.t. inclusion, of non-empty subset of prime ideals of commutative rings

The finite generation of $M$, to conclude $M$ is Noetherian (when $R$ is Noetherian).

Consequence of epimorphism from Noetherian $R$-module

If finite product of maximal ideals of ring $R$ is zero, then $R$ is Noetherian$\iff R$ is Artinian

Certain exact functor on the Grothendieck group of a module category

Noetherian module does not contain a submodule $N$ which is a direct sum of $n$ simple modules

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

Every Artinian ring is isomorphic to a direct product of Artinian local rings

Is the fiber product of local artinian rings again local artinian under these conditions?

If $V/F$ has basis $\{x_1,x_2,x_3,\dotsc\}$, $T'\colon V \to V$ is the right-shift operator, $W\subset V$ is $T'$-invariant, then $\dim V/W < \infty$?

Characterisation of Largest Semisimple Left Ideal

socle and essential extension of finitely generated mod over an artin algebra

Counterexample: Local Artinian ring is not a PID

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

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