Question

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

score 149 · Answer 1 · 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 38 · Answer 2 · 2019-05-08 15:41:16

38

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Let $(A, +, \cdot )$ be a ring such that $A/<x>$ is finite, for every $0 \neq x \in A$. Show that $A$ is noetherian.

Published on 08 May 2019 - 15:41

score 81 · Answer 3 · 2019-05-09 12:44:12

81

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depth $R_{\mathfrak p}=0$ implies $\mathfrak pR_{\mathfrak p}$ is associated to zero

Published on 09 May 2019 - 12:44

score 173 · Answer 4 · 2019-05-15 18:56:20

173

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Is a finitely generated subring of a Noetherian ring also Noetherian?

Published on 15 May 2019 - 18:56

score 171 · Answer 5 · 2019-05-30 17:46:00

171

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Flaw in the proof that $M$ is noetherian given exact sequence?

Published on 30 May 2019 - 17:46

score 199 · Answer 6 · 2019-06-04 07:39:44

199

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Depth of a local ring

Published on 04 Jun 2019 - 7:39

score 106 · Answer 7 · 2019-06-04 18:08:53

106

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Intersection of ideals equal to their product on noetherian ring

Published on 04 Jun 2019 - 18:08

score 193 · Answer 8 · 2019-06-13 09:07:04

193

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Converse of : If $M$ is Noetherian then $M_m$ is Noetherian for every $m\in\operatorname{Max}(R)$.

Published on 13 Jun 2019 - 9:07

score 131 · Answer 9 · 2019-06-25 21:47:40

131

Views

Atiyah Macdonald Exercise 6.2

Published on 25 Jun 2019 - 21:47

score 551 · Answer 10 · 2019-06-27 13:42:13

551

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Localization of Noetherian rings

Published on 27 Jun 2019 - 13:42

score 107 · Answer 11 · 2019-06-28 15:05:46

107

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Hilbert's basis theorem

Published on 28 Jun 2019 - 15:05

score 423 · Answer 12 · 2026-03-25 06:01:21

423

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Some sufficient condition for a Noetherian local ring to be a DVR

Published on 25 Mar 2026 - 6:01

score 241 · Answer 13 · 2019-07-02 10:28:49

241

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About noetherian commutative rings

Published on 02 Jul 2019 - 10:28

score 57 · Answer 14 · 2019-07-04 21:10:44

57

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Show That Function on Ideal is Just Multiplication Map

Published on 04 Jul 2019 - 21:10

score 127 · Answer 15 · 2026-03-25 06:04:36

127

Views

Systematic Way to find System of Parameters of Local Rings

Published on 25 Mar 2026 - 6:04

List Question

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

Let $(A, +, \cdot )$ be a ring such that $A/<x>$ is finite, for every $0 \neq x \in A$. Show that $A$ is noetherian.

depth $R_{\mathfrak p}=0$ implies $\mathfrak pR_{\mathfrak p}$ is associated to zero

Is a finitely generated subring of a Noetherian ring also Noetherian?

Flaw in the proof that $M$ is noetherian given exact sequence?

Depth of a local ring

Intersection of ideals equal to their product on noetherian ring

Converse of : If $M$ is Noetherian then $M_m$ is Noetherian for every $m\in\operatorname{Max}(R)$.

Atiyah Macdonald Exercise 6.2

Localization of Noetherian rings

Hilbert's basis theorem

Some sufficient condition for a Noetherian local ring to be a DVR

About noetherian commutative rings

Show That Function on Ideal is Just Multiplication Map

Systematic Way to find System of Parameters of Local Rings

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