List questions from localization

Published on 25 Mar 2026 - 17:37

66

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isomorphism for multiplicative systems

Published on 07 Jun 2021 - 17:29

316

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Atiyah & Macdonald, Problem 3.24

Published on 10 Jun 2021 - 21:59

124

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Regular functions on the domain of a regular function in an affine variety

Published on 12 Jun 2021 - 15:27

58

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$\text{Tor}_i^A(M,N) \cong \text{Tor}_i^{S^{-1}A}(M,N)$ for $S^{-1}A$-Modules $M,N$

Published on 14 Jun 2021 - 9:31

25

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Localization of integral domains is monotone

Published on 14 Jun 2021 - 9:33

157

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Show isomorphism between localization of rings

Published on 27 Mar 2026 - 4:16

164

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Prove that $S^{-1}M\otimes_{S^{-1}R} S^{-1}N=S^{-1}M\otimes_R S^{-1}N$

Published on 06 Jul 2021 - 11:20

95

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Let $R$ be a commutative ring, let $S\subset R$ and let $T$ be the smallest multiplicatively closed subset of $R$ containing $S$. Then $R_S\cong R_T$

Published on 06 Jul 2021 - 14:19

136

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Pullback of ring localizations.

Published on 24 Feb 2026 - 6:08

57

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Tensor product of $R_f$ by $R_g$

Published on 09 Jul 2021 - 22:52

149

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showing a ring is isomorphic to a localization of $R$ at $S$

Published on 11 Jul 2021 - 17:37

203

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Localization and field of fractions of an integral domain

Published on 13 Jul 2021 - 18:14

61

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Addition and multiplication in localization of a ring

Published on 14 Jul 2021 - 10:13

482

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Background on the $p$-adic valuation

Published on 28 Mar 2026 - 22:53

List Question

Ideals in localisation of graded ring

isomorphism for multiplicative systems

Atiyah & Macdonald, Problem 3.24

Regular functions on the domain of a regular function in an affine variety

$\text{Tor}_i^A(M,N) \cong \text{Tor}_i^{S^{-1}A}(M,N)$ for $S^{-1}A$-Modules $M,N$

Localization of integral domains is monotone

Show isomorphism between localization of rings

Prove that $S^{-1}M\otimes_{S^{-1}R} S^{-1}N=S^{-1}M\otimes_R S^{-1}N$

Let $R$ be a commutative ring, let $S\subset R$ and let $T$ be the smallest multiplicatively closed subset of $R$ containing $S$. Then $R_S\cong R_T$

Pullback of ring localizations.

Tensor product of $R_f$ by $R_g$

showing a ring is isomorphic to a localization of $R$ at $S$

Localization and field of fractions of an integral domain

Addition and multiplication in localization of a ring

Background on the $p$-adic valuation

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