Question

A principal ideal is prime in a coprime localization -- is it prime in the ring?

score 71 · Answer 1 · 2026-03-25 14:26:10

71

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A principal ideal is prime in a coprime localization -- is it prime in the ring?

Published on 25 Mar 2026 - 14:26

score 46 · Answer 2 · 2026-03-25 22:04:45

46

Views

Is Artinian assumption necessary here in Matsumura's book?

Published on 25 Mar 2026 - 22:04

score 57 · Answer 3 · 2023-10-12 15:45:26

57

Views

the case of Noetherian local ring

Published on 12 Oct 2023 - 15:45

score 149 · Answer 4 · 2023-10-14 04:41:20

149

Views

Proving a quotient ring is Noetherian.

Published on 14 Oct 2023 - 4:41

score 50 · Answer 5 · 2023-10-20 16:30:42

50

Views

Why does an injective $R$-module homomorphism $M\to N$ preserve submodules?

Published on 20 Oct 2023 - 16:30

score 71 · Answer 6 · 2023-10-21 21:53:14

71

Views

What are some standard generalisations of Noetherian rings?

Published on 21 Oct 2023 - 21:53

score 20 · Answer 7 · 2026-03-25 14:05:28

20

Views

counter-example for quotient of artinian and noetherian modules

Published on 25 Mar 2026 - 14:05

score 85 · Answer 8 · 2026-03-25 17:48:41

85

Views

Rings where finitely generated ideals are closed under countable intersection

Published on 25 Mar 2026 - 17:48

score 105 · Answer 9 · 2023-11-16 16:13:24

105

Views

Non-Noetherian ring that has an ideal $I$ containing a power of $\sqrt{I}$

Published on 16 Nov 2023 - 16:13

score 120 · Answer 10 · 2026-03-26 21:27:17

120

Views

Show that the ring of formal power series in a commutative ring $R$, $R[[x]]$ is noetherian.

Published on 26 Mar 2026 - 21:27

score 41 · Answer 11 · 2026-03-26 03:01:34

41

Views

Is the ideal of projective variety homogeneous when the projective variety is defined over a ring

Published on 26 Mar 2026 - 3:01

score 285 · Answer 12 · 2026-03-26 12:34:44

285

Views

Why is the noetherian ring property not definable in first-order logic?

Published on 26 Mar 2026 - 12:34

score 50 · Answer 13 · 2023-12-03 14:46:49

50

Views

On which rings must a finitely generated module be finitely presented? Is there an 'if and only if' characterization for such rings?

Published on 03 Dec 2023 - 14:46

score 46 · Answer 14 · 2023-12-08 08:51:21

46

Views

Dummit & Foote (3rd ed.) 15.1.11

Published on 08 Dec 2023 - 8:51

score 88 · Answer 15 · 2026-03-26 22:52:36

88

Views

Prove $\cap_{n\geq0} I^n = (0)$

Published on 26 Mar 2026 - 22:52

List Question

A principal ideal is prime in a coprime localization -- is it prime in the ring?

Is Artinian assumption necessary here in Matsumura's book?

the case of Noetherian local ring

Proving a quotient ring is Noetherian.

Why does an injective $R$-module homomorphism $M\to N$ preserve submodules?

What are some standard generalisations of Noetherian rings?

counter-example for quotient of artinian and noetherian modules

Rings where finitely generated ideals are closed under countable intersection

Non-Noetherian ring that has an ideal $I$ containing a power of $\sqrt{I}$

Show that the ring of formal power series in a commutative ring $R$, $R[[x]]$ is noetherian.

Is the ideal of projective variety homogeneous when the projective variety is defined over a ring

Why is the noetherian ring property not definable in first-order logic?

On which rings must a finitely generated module be finitely presented? Is there an 'if and only if' characterization for such rings?

Dummit & Foote (3rd ed.) 15.1.11

Prove $\cap_{n\geq0} I^n = (0)$

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