Question

Localising a ring twice gives ring isomorphic to localising by each subset in turn

score 55 · Answer 1 · 2026-03-26 11:05:04

55

Views

Localising a ring twice gives ring isomorphic to localising by each subset in turn

Published on 26 Mar 2026 - 11:05

score 85 · Answer 2 · 2023-05-22 10:09:23

85

Views

Intuitively, why $\operatorname{spec}(S^{-1}A) \cong \lbrace \mathfrak{p} \in \operatorname{spec} (A)| \mathfrak{p} \cap S = \emptyset \rbrace$?

Published on 22 May 2023 - 10:09

score 143 · Answer 3 · 2026-03-25 18:56:15

143

Views

stalk isomorphism + homeomorphism = isomorphism of varieties

Published on 25 Mar 2026 - 18:56

score 76 · Answer 4 · 2023-05-24 17:31:51

76

Views

Sheaf topos is localisation at covering sieve inclusion

Published on 24 May 2023 - 17:31

score 177 · Answer 5 · 2023-06-05 18:11:52

177

Views

Is the localization at a prime ideal of any polynomial ring always a valuation ring?

Published on 05 Jun 2023 - 18:11

score 62 · Answer 6 · 2023-06-05 20:03:22

62

Views

Is the localization of a polynomial ring at a prime ideal a valuation ring if and only if the prime ideal is principal?

Published on 05 Jun 2023 - 20:03

score 167 · Answer 7 · 2023-06-09 02:56:27

167

Views

Is testing whether the nonunits of $K[x,y]_{(x,y)}[1/y]$ form an ideal a messy undertaking or am I going about it wrong?

Published on 09 Jun 2023 - 2:56

score 63 · Answer 8 · 2026-03-26 08:31:17

63

Views

Dimension of a positively graded ring after a suitable localization

Published on 26 Mar 2026 - 8:31

score 154 · Answer 9 · 2026-03-26 17:53:24

154

Views

Scheme theoretic fiber vs. Degree of a point of a finite morphism of affine schemes

Published on 26 Mar 2026 - 17:53

score 92 · Answer 10 · 2023-06-18 18:40:02

92

Views

A normal ring (possibly a non-domain) is integrally closed in its total ring of fractions

Published on 18 Jun 2023 - 18:40

score 99 · Answer 11 · 2026-03-25 18:57:43

99

Views

Multiplicity of intersection of $y^2=x^3$ and $x^2=y^3$ at the origin

Published on 25 Mar 2026 - 18:57

score 38 · Answer 12 · 2023-07-07 13:00:21

38

Views

Ring of formal multivariate Laurent series as a consecutive localisation

Published on 07 Jul 2023 - 13:00

score 46 · Answer 13 · 2023-07-24 19:22:59

46

Views

$B/\mathfrak p B\cong B_\mathfrak p/\mathfrak p B_\mathfrak p$ for Dedekind extensions $A\subseteq B$ and primes $(0)\ne\mathfrak p\subset A$

Published on 24 Jul 2023 - 19:22

score 164 · Answer 14 · 2023-07-25 20:24:43

164

Views

Why $S^{-1}R$ is called localization, despite $S^{-1}R$ is not always local ring?

Published on 25 Jul 2023 - 20:24

score 50 · Answer 15 · 2026-03-26 14:18:44

50

Views

Functor with two successive adjoints is a localization

Published on 26 Mar 2026 - 14:18

List Question

Localising a ring twice gives ring isomorphic to localising by each subset in turn

Intuitively, why $\operatorname{spec}(S^{-1}A) \cong \lbrace \mathfrak{p} \in \operatorname{spec} (A)| \mathfrak{p} \cap S = \emptyset \rbrace$?

stalk isomorphism + homeomorphism = isomorphism of varieties

Sheaf topos is localisation at covering sieve inclusion

Is the localization at a prime ideal of any polynomial ring always a valuation ring?

Is the localization of a polynomial ring at a prime ideal a valuation ring if and only if the prime ideal is principal?

Is testing whether the nonunits of $K[x,y]_{(x,y)}[1/y]$ form an ideal a messy undertaking or am I going about it wrong?

Dimension of a positively graded ring after a suitable localization

Scheme theoretic fiber vs. Degree of a point of a finite morphism of affine schemes

A normal ring (possibly a non-domain) is integrally closed in its total ring of fractions

Multiplicity of intersection of $y^2=x^3$ and $x^2=y^3$ at the origin

Ring of formal multivariate Laurent series as a consecutive localisation

$B/\mathfrak p B\cong B_\mathfrak p/\mathfrak p B_\mathfrak p$ for Dedekind extensions $A\subseteq B$ and primes $(0)\ne\mathfrak p\subset A$

Why $S^{-1}R$ is called localization, despite $S^{-1}R$ is not always local ring?

Functor with two successive adjoints is a localization

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