Question

Exactness of sequences of modules is a local property

score 2.5k · Answer 1 · 2012-03-17 01:23:19

2.5k

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Exactness of sequences of modules is a local property

Published on 17 Mar 2012 - 1:23

score 7.8k · Answer 2 · 2012-05-02 23:33:23

7.8k

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Show that the ring of all rational numbers, which when written in simplest form has an odd denominator, is a principal ideal domain.

Published on 02 May 2012 - 23:33

score 830 · Answer 3 · 2012-05-20 14:38:45

830

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Does the contraction from the localized ring preserve colon ideals and ideal sums/products?

Published on 20 May 2012 - 14:38

score 5.4k · Answer 4 · 2012-05-31 22:12:51

5.4k

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Localisation is isomorphic to a quotient of polynomial ring

Published on 31 May 2012 - 22:12

score 1.9k · Answer 5 · 2026-03-26 10:58:33

1.9k

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Localization of a non-commutative ring

Published on 26 Mar 2026 - 10:58

score 1.8k · Answer 6 · 2012-10-04 06:43:31

1.8k

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Localization at an element is intersection of localizations at primes not containing the element

Published on 04 Oct 2012 - 6:43

score 1.7k · Answer 7 · 2013-01-26 11:08:17

1.7k

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Subrings of fraction fields

Published on 26 Jan 2013 - 11:08

score 23k · Answer 8 · 2013-02-11 19:05:05

23k

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Why is the localization at a prime ideal a local ring?

Published on 11 Feb 2013 - 19:05

score 973 · Answer 9 · 2013-02-19 13:04:18

973

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When is the localization of a module trivial?

Published on 19 Feb 2013 - 13:04

score 560 · Answer 10 · 2013-03-11 09:36:38

560

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Fraction equivalence is transitive in localizations (general non-domain case)

Published on 11 Mar 2013 - 9:36

score 575 · Answer 11 · 2020-07-31 16:13:15

575

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Question about the sheaf of differentials of a fibre

Published on 31 Jul 2020 - 16:13

score 215 · Answer 12 · 2020-08-01 07:45:12

215

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Intuition for fractions of the localization of a non integral domain

Published on 01 Aug 2020 - 7:45

score 165 · Answer 13 · 2020-08-02 22:05:41

165

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Let $R$ be an integral domain and let $S={\rm Frac}(R)$. Do we always have $R(x)=S(x)$?

Published on 02 Aug 2020 - 22:05

score 378 · Answer 14 · 2026-03-27 10:30:14

378

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Module is flat over localization

Published on 27 Mar 2026 - 10:30

score 226 · Answer 15 · 2026-03-27 13:25:27

226

Views

How do I finish computing the associated graded ring of the localized ring $k[x]_{(x)}$ at its maximal ideal $(x)_{(x)}$?

Published on 27 Mar 2026 - 13:25

List Question

Exactness of sequences of modules is a local property

Show that the ring of all rational numbers, which when written in simplest form has an odd denominator, is a principal ideal domain.

Does the contraction from the localized ring preserve colon ideals and ideal sums/products?

Localisation is isomorphic to a quotient of polynomial ring

Localization of a non-commutative ring

Localization at an element is intersection of localizations at primes not containing the element

Subrings of fraction fields

Why is the localization at a prime ideal a local ring?

When is the localization of a module trivial?

Fraction equivalence is transitive in localizations (general non-domain case)

Question about the sheaf of differentials of a fibre

Intuition for fractions of the localization of a non integral domain

Let $R$ be an integral domain and let $S={\rm Frac}(R)$. Do we always have $R(x)=S(x)$?

Module is flat over localization

How do I finish computing the associated graded ring of the localized ring $k[x]_{(x)}$ at its maximal ideal $(x)_{(x)}$?

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