List questions from localization

Published on 25 Mar 2026 - 11:54

84

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When does localisation behave badly?

Published on 03 Dec 2018 - 11:42

150

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

Published on 03 Dec 2018 - 12:52

96

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Valuation ring and localizations

Published on 25 Mar 2026 - 11:17

146

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

Published on 08 Dec 2018 - 12:52

239

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localization of a polynomial ring at a prime ideal

Published on 09 Dec 2018 - 16:40

72

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

Published on 12 Dec 2018 - 16:28

2.2k

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When is the localization map injective?

Published on 14 Dec 2018 - 17:56

51

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Integrally closed domains, where is the reduced hypothesis used?

Published on 16 Dec 2018 - 13:26

169

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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 19 Dec 2018 - 11:54

107

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Question regarding localization of polynomial ring

Published on 22 Dec 2018 - 20:41

40

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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 30 Dec 2018 - 8:32

563

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

Published on 10 Jan 2019 - 4:45

97

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

Published on 13 Jan 2019 - 12:04

900

Views

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

Published on 17 Jan 2019 - 9:21

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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