Question

Show that the localization $\mathbb{R}[x]_{(x-1)}$ is not an integral extension of $\mathbb{R}[x^2 -1]_{(x-1)\cap \mathbb{R}[x^2-1]}$

score 204 · Answer 1 · 2020-12-04 02:00:35

Show that the localization $\mathbb{R}[x]_{(x-1)}$ is not an integral extension of $\mathbb{R}[x^2 -1]_{(x-1)\cap \mathbb{R}[x^2-1]}$

score 426 · Answer 2 · 2020-12-07 15:02:27

426

Views

Localization is finitely generated implies, that multiplicative group only contains invertible elements

Published on 07 Dec 2020 - 15:02

score 68 · Answer 3 · 2020-12-10 19:35:50

68

Views

If $R$ is not integral domain, and $P$ is prime in $R$, is $P^e$ not equal to $PR_P$?

Published on 10 Dec 2020 - 19:35

score 161 · Answer 4 · 2020-12-11 21:55:23

161

Views

Adjoining an inverse to a central element of an algebra

Published on 11 Dec 2020 - 21:55

score 106 · Answer 5 · 2026-03-29 03:36:06

106

Views

Give an example of a local domain with principal maximal ideal, which is not a valuation ring

Published on 29 Mar 2026 - 3:36

score 121 · Answer 6 · 2026-03-27 13:41:08

121

Views

Prime ideals of localization of absolutely flat modules

Published on 27 Mar 2026 - 13:41

score 99 · Answer 7 · 2020-12-19 03:13:04

99

Views

The ring homomorphism between a commutative ring $R$ and its localization $S^{-1}R$ is invertible on $S$

Published on 19 Dec 2020 - 3:13

score 124 · Answer 8 · 2020-12-22 01:47:34

124

Views

Finite free resolutions of modules over coordinate ring of smooth elliptic curve over $\mathbb{C}$

Published on 22 Dec 2020 - 1:47

score 167 · Answer 9 · 2026-03-28 20:07:51

167

Views

Limits in the localization of a category of fibrant objects

Published on 28 Mar 2026 - 20:07

score 513 · Answer 10 · 2026-03-27 23:57:28

513

Views

Atiyah-Macdonald: Exercise 3.5

Published on 27 Mar 2026 - 23:57

score 105 · Answer 11 · 2026-03-28 02:04:47

105

Views

Can the category of S-local objects be reflective but not a localization by S?

Published on 28 Mar 2026 - 2:04

score 110 · Answer 12 · 2020-12-28 07:18:46

110

Views

the number of distinct subrings of $\mathbb{Q}$ is infinite without using infiniteness of prime numbers

Published on 28 Dec 2020 - 7:18

score 396 · Answer 13 · 2020-12-31 14:15:20

396

Views

Show that the following localization ring has one maximal ideal

Published on 31 Dec 2020 - 14:15

score 86 · Answer 14 · 2026-03-28 14:05:27

86

Views

$O_{K,\mathfrak{p}} = \Bbb{Z}[a]_{(p,\pi)}$ when $O_K$ is non-monogenic

Published on 28 Mar 2026 - 14:05

score 84 · Answer 15 · 2021-01-02 17:56:00

84

Views

Computing localizations in $\mathbb{Z}/n\mathbb{Z}$

Published on 02 Jan 2021 - 17:56

List Question

Show that the localization $\mathbb{R}[x]_{(x-1)}$ is not an integral extension of $\mathbb{R}[x^2 -1]_{(x-1)\cap \mathbb{R}[x^2-1]}$

Localization is finitely generated implies, that multiplicative group only contains invertible elements

If $R$ is not integral domain, and $P$ is prime in $R$, is $P^e$ not equal to $PR_P$?

Adjoining an inverse to a central element of an algebra

Give an example of a local domain with principal maximal ideal, which is not a valuation ring

Prime ideals of localization of absolutely flat modules

The ring homomorphism between a commutative ring $R$ and its localization $S^{-1}R$ is invertible on $S$

Finite free resolutions of modules over coordinate ring of smooth elliptic curve over $\mathbb{C}$

Limits in the localization of a category of fibrant objects

Atiyah-Macdonald: Exercise 3.5

Can the category of S-local objects be reflective but not a localization by S?

the number of distinct subrings of $\mathbb{Q}$ is infinite without using infiniteness of prime numbers

Show that the following localization ring has one maximal ideal

$O_{K,\mathfrak{p}} = \Bbb{Z}[a]_{(p,\pi)}$ when $O_K$ is non-monogenic

Computing localizations in $\mathbb{Z}/n\mathbb{Z}$

Trending Questions

Popular # Hahtags

Popular Questions