List questions from localization

Published on 16 Nov 2017 - 23:57

70

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Is the hypothesis of this problem enough to prove it? Universal property of localization

Published on 27 Mar 2026 - 6:08

744

Views

A criterion for a module over a local ring to be of finite length

Published on 28 Mar 2026 - 13:41

157

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Prove that $A/mA \cong A_m/mR_m A_m$.

Published on 20 Nov 2017 - 17:17

90

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$\phi: A\to A_S$ is an embedding for every multiplicatively closed set S $\implies$ A is integral

Published on 28 Mar 2026 - 13:40

416

Views

Homogeneous localization and field of fractions

Published on 28 Nov 2017 - 16:43

333

Views

Is $k[x]_{(x)}$ never isomorphic with $k[[x]]$?

Published on 27 Mar 2026 - 16:03

340

Views

About the localization of a euclidean domain

Published on 27 Mar 2026 - 2:23

2.1k

Views

Localization with respect to a multiplicative set containing zero divisors

Published on 04 Dec 2017 - 11:07

189

Views

Prove that $(S^{-1}R)[x] \cong S^{-1}(R[x])$.

Published on 09 Dec 2017 - 7:28

744

Views

Isomorphism between localizations of $\mathbb{Z}[\sqrt{-5}]$ and ideal $\langle 2, 1 + \sqrt{-5} \rangle$ at some prime ideal

Published on 11 Dec 2017 - 1:14

1.6k

Views

Why a short sequence of modules is exact if and only if the short sequence of their localization at any prime ideal is exact?

Published on 14 Dec 2017 - 17:42

45

Views

Localisation with respect to $H \mathbb{Q}$

Published on 26 Mar 2026 - 3:18

435

Views

Fiber product in the category of DG categories

Published on 15 Dec 2017 - 14:24

1.2k

Views

nilpotent elements in a localization of a commutative Ring

Published on 27 Mar 2026 - 18:48

List Question

Localization of a quotient ring

Is the hypothesis of this problem enough to prove it? Universal property of localization

A criterion for a module over a local ring to be of finite length

Prove that $A/mA \cong A_m/mR_m A_m$.

$\phi: A\to A_S$ is an embedding for every multiplicatively closed set S $\implies$ A is integral

Homogeneous localization and field of fractions

Is $k[x]_{(x)}$ never isomorphic with $k[[x]]$?

About the localization of a euclidean domain

Localization with respect to a multiplicative set containing zero divisors

Prove that $(S^{-1}R)[x] \cong S^{-1}(R[x])$.

Isomorphism between localizations of $\mathbb{Z}[\sqrt{-5}]$ and ideal $\langle 2, 1 + \sqrt{-5} \rangle$ at some prime ideal

Why a short sequence of modules is exact if and only if the short sequence of their localization at any prime ideal is exact?

Localisation with respect to $H \mathbb{Q}$

Fiber product in the category of DG categories

nilpotent elements in a localization of a commutative Ring

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