Question

Show that $(a, x) \sim (b, y) \iff w(ay - bx) = 0, \text{ for some } w \in S$ defines an equivalence relation on $R \times S$.

score 51 · Answer 1 · 2020-08-10 19:29:11

51

Views

Show that $(a, x) \sim (b, y) \iff w(ay - bx) = 0, \text{ for some } w \in S$ defines an equivalence relation on $R \times S$.

Published on 10 Aug 2020 - 19:29

score 88 · Answer 2 · 2020-08-12 09:16:07

88

Views

An 'away sheaf' on the scheme of a PID: Localize at powers of the generator of the prime ideal?

Published on 12 Aug 2020 - 9:16

score 543 · Answer 3 · 2020-08-13 18:04:28

543

Views

Localization of finitely generated torsion-free module over Noetherian ring (not necessarily an integral domain)

Published on 13 Aug 2020 - 18:04

score 246 · Answer 4 · 2026-03-27 19:55:03

246

Views

Can the structure sheaf of the spectrum of a ring be defined by taking appropriate localizations on every open set?

Published on 27 Mar 2026 - 19:55

score 92 · Answer 5 · 2026-03-28 15:26:32

92

Views

Local behaviour of a module localized at a prime ideal

Published on 28 Mar 2026 - 15:26

score 139 · Answer 6 · 2020-08-17 00:35:03

139

Views

Proving that $(M \otimes_A N)_q = M_p \otimes_{A_p} N_q$ for a prime $q$ lying over $p$

Published on 17 Aug 2020 - 0:35

score 115 · Answer 7 · 2020-08-19 01:42:04

115

Views

The maximal ideal of $\mathbb{Z}_{(p)}[x]$ which contains ideal $I＝(x^2＋1)$ contains $p$

Published on 19 Aug 2020 - 1:42

score 697 · Answer 8 · 2020-08-21 17:57:11

697

Views

Determining the local ring of a curve

Published on 21 Aug 2020 - 17:57

score 164 · Answer 9 · 2026-03-31 05:39:59

164

Views

Exactness of sequence and localization

Published on 31 Mar 2026 - 5:39

score 98 · Answer 10 · 2020-08-29 16:12:50

98

Views

Atiyah Proposition $3.5$ - Scalar multiplication issue.

Published on 29 Aug 2020 - 16:12

score 33 · Answer 11 · 2026-03-27 01:46:00

33

Views

How to determine direction of arrival, given TDoA?

Published on 27 Mar 2026 - 1:46

score 43 · Answer 12 · 2026-03-26 22:53:15

43

Views

Examples of local ring with principal group units $U_{1}=U_{1}^{2}$

Published on 26 Mar 2026 - 22:53

score 86 · Answer 13 · 2020-10-06 15:14:16

86

Views

What is the fraction field of $A[z]/(z^2-f)$?

Published on 06 Oct 2020 - 15:14

score 108 · Answer 14 · 2020-10-11 19:59:15

108

Views

How is the canonical localization isomorphism $M_U\cong M\otimes_R R_U$ an isomorphism of $R_U$-modules?

Published on 11 Oct 2020 - 19:59

score 51 · Answer 15 · 2020-10-19 13:40:47

51

Views

Show that $M_m \neq 0$ for $m = (x, y - 1)$ where $A=k[x,y]$ and $M=k[x,y]/(x)$

Published on 19 Oct 2020 - 13:40

List Question

Show that $(a, x) \sim (b, y) \iff w(ay - bx) = 0, \text{ for some } w \in S$ defines an equivalence relation on $R \times S$.

An 'away sheaf' on the scheme of a PID: Localize at powers of the generator of the prime ideal?

Localization of finitely generated torsion-free module over Noetherian ring (not necessarily an integral domain)

Can the structure sheaf of the spectrum of a ring be defined by taking appropriate localizations on every open set?

Local behaviour of a module localized at a prime ideal

Proving that $(M \otimes_A N)_q = M_p \otimes_{A_p} N_q$ for a prime $q$ lying over $p$

The maximal ideal of $\mathbb{Z}_{(p)}[x]$ which contains ideal $I＝(x^2＋1)$ contains $p$

Determining the local ring of a curve

Exactness of sequence and localization

Atiyah Proposition $3.5$ - Scalar multiplication issue.

How to determine direction of arrival, given TDoA?

Examples of local ring with principal group units $U_{1}=U_{1}^{2}$

What is the fraction field of $A[z]/(z^2-f)$?

How is the canonical localization isomorphism $M_U\cong M\otimes_R R_U$ an isomorphism of $R_U$-modules?

Show that $M_m \neq 0$ for $m = (x, y - 1)$ where $A=k[x,y]$ and $M=k[x,y]/(x)$

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