List questions from localization

Published on 29 Sep 2018 - 14:54

1k

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What is the difference between a directed set and a filtered category?

Published on 25 Mar 2026 - 3:18

272

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What is the definition of a localization of a category?

Published on 25 Mar 2026 - 5:07

43

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Two definitions of a local property of rings and modules.

Published on 05 Oct 2018 - 13:44

149

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The localization of a commutative ring with unity

Published on 13 Oct 2018 - 13:42

801

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An isomorphism between the residue field and the fraction field

Published on 13 Oct 2018 - 14:24

69

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Global sections of pullback of $G$-equivariant $D_Z$-modules

Published on 23 Mar 2026 - 8:49

49

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Are the following definitions of a local property equivalent?

Published on 19 Oct 2018 - 7:42

24

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What is the induced $G$-action on the localization $S^{-1} A$?

Published on 25 Mar 2026 - 20:42

35

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What is $S^{-1}N$ in $S^{-1}M$?

Published on 22 Oct 2018 - 10:43

485

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A question about $S^{-1}R\otimes_R M\cong S^{-1}M$ as $S^{-1}R$-modules

Published on 23 Oct 2018 - 2:27

124

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Minimal prime of a ring is contraction of some prime ideal of any extension of the ring.

Published on 23 Oct 2018 - 19:44

139

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For $m \in \text{max} \ R[X]$ and $f \in R[X] \setminus m, \ R[X]_f$ is not a local ring

Published on 25 Oct 2018 - 10:39

554

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On derived categories of exact categories

Published on 22 Mar 2026 - 11:48

122

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When does it suffice to show statements about rings only for the local ring after localizing at a prime?

Published on 04 Nov 2018 - 13:11

List Question

Localization of Tensor

What is the difference between a directed set and a filtered category?

What is the definition of a localization of a category?

Two definitions of a local property of rings and modules.

The localization of a commutative ring with unity

An isomorphism between the residue field and the fraction field

Global sections of pullback of $G$-equivariant $D_Z$-modules

Are the following definitions of a local property equivalent?

What is the induced $G$-action on the localization $S^{-1} A$?

What is $S^{-1}N$ in $S^{-1}M$?

A question about $S^{-1}R\otimes_R M\cong S^{-1}M$ as $S^{-1}R$-modules

Minimal prime of a ring is contraction of some prime ideal of any extension of the ring.

For $m \in \text{max} \ R[X]$ and $f \in R[X] \setminus m, \ R[X]_f$ is not a local ring

On derived categories of exact categories

When does it suffice to show statements about rings only for the local ring after localizing at a prime?

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