List questions from localization

Published on 10 May 2026 - 13:51

87

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When does localisation behave badly?

Published on 11 Apr 2026 - 6:08

153

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Localisation of $\mathbb{Z}/(p^k)$.

Published on 12 Apr 2026 - 9:04

100

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Valuation ring and localizations

Published on 10 May 2026 - 15:07

148

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Let $R \subseteq S$ be two local PIDs with the same field of fractions, then $R=S$.

Published on 13 Apr 2026 - 16:13

242

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localization of a polynomial ring at a prime ideal

Published on 14 Apr 2026 - 1:45

75

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Question about the ring $A_P$ of regular functions on a variety $V$

Published on 14 Apr 2026 - 11:13

2.2k

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When is the localization map injective?

Published on 13 Apr 2026 - 12:28

54

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Integrally closed domains, where is the reduced hypothesis used?

Published on 16 Apr 2026 - 0:38

172

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What does it mean for localization to be same if multiplicative set is different? $T^{-1}R = S^{-1}R$?

Published on 13 Apr 2026 - 16:07

110

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Question regarding localization of polynomial ring

Published on 15 Apr 2026 - 14:26

43

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$R_p$ is a field iff for any $x \in p$ there exists $y \not\in p$ such that $xy = 0$

Published on 13 Apr 2026 - 22:36

566

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Prove $R_{\mathfrak p}$ has only one maximal ideal $\mathfrak pR_{\mathfrak p}$

Published on 15 Apr 2026 - 3:17

100

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Does $\frac{b}{s} \in S^{-1} I$ directly implies that $b \in I$?

Published on 12 Apr 2026 - 2:39

903

Views

Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set

Published on 14 Apr 2026 - 1:32

List Question

Isomorphism between localizations of graded ring $S_{(P)} \cong [S_{(f)}]_{PS_f \cap S_{(f)}}$

When does localisation behave badly?

Localisation of $\mathbb{Z}/(p^k)$.

Valuation ring and localizations

Let $R \subseteq S$ be two local PIDs with the same field of fractions, then $R=S$.

localization of a polynomial ring at a prime ideal

Question about the ring $A_P$ of regular functions on a variety $V$

When is the localization map injective?

Integrally closed domains, where is the reduced hypothesis used?

What does it mean for localization to be same if multiplicative set is different? $T^{-1}R = S^{-1}R$?

Question regarding localization of polynomial ring

$R_p$ is a field iff for any $x \in p$ there exists $y \not\in p$ such that $xy = 0$

Prove $R_{\mathfrak p}$ has only one maximal ideal $\mathfrak pR_{\mathfrak p}$

Does $\frac{b}{s} \in S^{-1} I$ directly implies that $b \in I$?

Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set

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