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Questions in the proof that every minimal prime ideal in A is contained in Z(A)

score 24 · Answer 1 · 2022-05-27 17:16:48

24

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Questions in the proof that every minimal prime ideal in A is contained in Z(A)

Published on 27 May 2022 - 17:16

score 94 · Answer 2 · 2026-03-28 17:41:16

94

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On Proposition $13.27$ of Adamek: full reflective subcategories are limits closed iff they are replete?

Published on 28 Mar 2026 - 17:41

score 455 · Answer 3 · 2026-03-30 03:54:58

455

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Two equivalent conditions on Serre's normality criterion

Published on 30 Mar 2026 - 3:54

score 222 · Answer 4 · 2026-03-26 01:18:01

222

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Proof explanation) Finite injective dimension of the residue field of a Noetherian local ring implies regularity

Published on 26 Mar 2026 - 1:18

score 64 · Answer 5 · 2022-06-01 16:09:45

64

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Definition of localization of a ring is slightly redundant

Published on 01 Jun 2022 - 16:09

score 19 · Answer 6 · 2026-03-27 16:25:20

19

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Prove $U^{-1}R \cong R[\{X_s\}_{s \in U}]/(sX_s - 1).$

Published on 27 Mar 2026 - 16:25

score 251 · Answer 7 · 2022-06-06 21:32:38

251

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Isomorphism between $R_p/pR_p$ and $\text{Frac}(R/p)$ is unique

Published on 06 Jun 2022 - 21:32

score 46 · Answer 8 · 2022-06-07 18:22:54

46

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How do I find all prime ideals of the localization $S^{-1}\Bbb{C}[X,Y]$ where $S=\{X^iY^j:i,j\in \Bbb{N}\}$?

Published on 07 Jun 2022 - 18:22

score 99 · Answer 9 · 2026-04-01 03:11:45

99

Views

Interpreting notation: showing localization commutes with finite product.

Published on 01 Apr 2026 - 3:11

score 29 · Answer 10 · 2022-06-15 06:52:22

29

Views

Why can we view $N$ as an $S^{-1}R$-module but also as an $R$ module, where $S$ is a multiplicative set?

Published on 15 Jun 2022 - 6:52

score 54 · Answer 11 · 2026-03-25 14:46:55

54

Views

Partition of Unity in Ismagilov-Morgan-Simon Formula of Localization on complete Riemannian non-compact manifolds

Published on 25 Mar 2026 - 14:46

score 212 · Answer 12 · 2022-07-02 09:07:49

212

Views

Why doesn't the condition $a/s=b/t$ iff $at=bs$ suffice when defining localization of commutative rings?

Published on 02 Jul 2022 - 9:07

score 57 · Answer 13 · 2026-03-28 07:58:46

57

Views

How to show localization induces a topological embedding on Spec?

Published on 28 Mar 2026 - 7:58

score 100 · Answer 14 · 2022-07-11 05:27:40

100

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Are every scheme's structure sheaf's restrictions to $U$ from the global sections given by localizing by functions nonvanishing on $U$?

Published on 11 Jul 2022 - 5:27

score 130 · Answer 15 · 2022-07-21 22:15:12

130

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The localisation of a ring over the non-zero divisors is the quotient field of this ring

Published on 21 Jul 2022 - 22:15

List Question

Questions in the proof that every minimal prime ideal in A is contained in Z(A)

On Proposition $13.27$ of Adamek: full reflective subcategories are limits closed iff they are replete?

Two equivalent conditions on Serre's normality criterion

Proof explanation) Finite injective dimension of the residue field of a Noetherian local ring implies regularity

Definition of localization of a ring is slightly redundant

Prove $U^{-1}R \cong R[\{X_s\}_{s \in U}]/(sX_s - 1).$

Isomorphism between $R_p/pR_p$ and $\text{Frac}(R/p)$ is unique

How do I find all prime ideals of the localization $S^{-1}\Bbb{C}[X,Y]$ where $S=\{X^iY^j:i,j\in \Bbb{N}\}$?

Interpreting notation: showing localization commutes with finite product.

Why can we view $N$ as an $S^{-1}R$-module but also as an $R$ module, where $S$ is a multiplicative set?

Partition of Unity in Ismagilov-Morgan-Simon Formula of Localization on complete Riemannian non-compact manifolds

Why doesn't the condition $a/s=b/t$ iff $at=bs$ suffice when defining localization of commutative rings?

How to show localization induces a topological embedding on Spec?

Are every scheme's structure sheaf's restrictions to $U$ from the global sections given by localizing by functions nonvanishing on $U$?

The localisation of a ring over the non-zero divisors is the quotient field of this ring

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