Question

Examples of modules that $M_\mathfrak{p} \subset N_\mathfrak{p}$ that does not imply $M \subset N$?

score 131 · Answer 1 · 2026-03-27 08:41:57

131

Views

Examples of modules that $M_\mathfrak{p} \subset N_\mathfrak{p}$ that does not imply $M \subset N$?

Published on 27 Mar 2026 - 8:41

score 121 · Answer 2 · 2021-07-30 08:45:20

121

Views

Is the colimit of regular rings still regular?

Published on 30 Jul 2021 - 8:45

score 151 · Answer 3 · 2021-08-04 14:14:10

151

Views

when localization is finite

Published on 04 Aug 2021 - 14:14

score 121 · Answer 4 · 2026-03-29 11:50:09

121

Views

Let $A$ be an integrally closed noetherian domain, and $(R, \mathfrak{m})$ local with $A \subseteq R \subseteq K(A)$. Is $R$ a localization of $A$?

Published on 29 Mar 2026 - 11:50

score 202 · Answer 5 · 2021-08-22 21:19:26

202

Views

Geometric meaning of localization at $(1+I)$?

Published on 22 Aug 2021 - 21:19

score 220 · Answer 6 · 2026-03-26 03:01:25

220

Views

Maximal Cohen-Macaulay modules of full support, over non-artinian local Cohen-Macaulay rings, are faithful?

Published on 26 Mar 2026 - 3:01

score 59 · Answer 7 · 2021-08-27 16:21:43

59

Views

Localization of a $\mathfrak p$-primary submodule

Published on 27 Aug 2021 - 16:21

score 155 · Answer 8 · 2021-08-27 19:45:49

Show that every non-zero ideal of the localization $\mathbb{Z}_{(p)}$ of $\mathbb{Z}$ at a prime $p$ is of the form $(p^n)$ for some $n \geq 0$

score 232 · Answer 9 · 2026-03-25 14:21:11

232

Views

A zero-divisor whose every localization is zero in a Noetherian ring whose every associated prime is minimal

Published on 25 Mar 2026 - 14:21

score 87 · Answer 10 · 2021-09-01 18:16:52

87

Views

$A$ be a domain and $S \subset A$ be an mcs, for $\alpha$ integral over $A$ is it true $S^{-1}A[\alpha]\cong(S^{-1}A)[\alpha]$?

Published on 01 Sep 2021 - 18:16

score 160 · Answer 11 · 2021-09-05 07:47:31

160

Views

local martingale and submartingale

Published on 05 Sep 2021 - 7:47

score 115 · Answer 12 · 2021-09-07 07:32:23

115

Views

Localization-induced homomorphism

Published on 07 Sep 2021 - 7:32

score 73 · Answer 13 · 2026-03-25 14:25:11

73

Views

If $x\in I$ is such that $\text{Supp}(0:_M x)\subseteq V(I)$ , then how to show that $x \notin \cup_{P\in \text{Ass}_R(M)\setminus V(I)} P $?

Published on 25 Mar 2026 - 14:25

score 80 · Answer 14 · 2026-03-29 02:30:32

80

Views

Relating prime spots and prime ideals in number fields

Published on 29 Mar 2026 - 2:30

score 82 · Answer 15 · 2026-03-29 13:24:23

82

Views

When an element of the total ring of fractions of a noetherian local ring $R$ is integral over $R$?

Published on 29 Mar 2026 - 13:24

List Question

Examples of modules that $M_\mathfrak{p} \subset N_\mathfrak{p}$ that does not imply $M \subset N$?

Is the colimit of regular rings still regular?

when localization is finite

Let $A$ be an integrally closed noetherian domain, and $(R, \mathfrak{m})$ local with $A \subseteq R \subseteq K(A)$. Is $R$ a localization of $A$?

Geometric meaning of localization at $(1+I)$?

Maximal Cohen-Macaulay modules of full support, over non-artinian local Cohen-Macaulay rings, are faithful?

Localization of a $\mathfrak p$-primary submodule

Show that every non-zero ideal of the localization $\mathbb{Z}_{(p)}$ of $\mathbb{Z}$ at a prime $p$ is of the form $(p^n)$ for some $n \geq 0$

A zero-divisor whose every localization is zero in a Noetherian ring whose every associated prime is minimal

$A$ be a domain and $S \subset A$ be an mcs, for $\alpha$ integral over $A$ is it true $S^{-1}A[\alpha]\cong(S^{-1}A)[\alpha]$?

local martingale and submartingale

Localization-induced homomorphism

If $x\in I$ is such that $\text{Supp}(0:_M x)\subseteq V(I)$ , then how to show that $x \notin \cup_{P\in \text{Ass}_R(M)\setminus V(I)} P $?

Relating prime spots and prime ideals in number fields

When an element of the total ring of fractions of a noetherian local ring $R$ is integral over $R$?

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