List questions from commutative-algebra

304

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Does every closed subset of the underlying space of a Noetherian scheme admits a natural closed subscheme structure?

Published on 27 Mar 2026 - 7:50

75

Views

quotient ring which is not local

Published on 11 Apr 2026 - 9:23

385

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Direct Limit of Both Rings and Their Modules

Published on 25 Mar 2026 - 14:39

55

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About a localization

Published on 09 Apr 2026 - 11:53

541

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Showing that $R[x_1,...,x_n]$ is the only $R$-algebra up to isomorphism that satisfies the universal property of the polynomial ring.

Published on 05 Jul 2019 - 15:14

90

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Demystify the Hilbert Function

Published on 06 Apr 2026 - 5:29

127

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Systematic Way to find System of Parameters of Local Rings

Published on 25 Mar 2026 - 6:04

172

Views

Show that the ideal $((x_1-\alpha_1)^{t_1},...,(x_n-\alpha_n)^{t_n})$ is primary.

Published on 25 Mar 2026 - 23:09

156

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Building the Henselization from above: J.S. Milne, Étale Cohomology (PMS-33), Exercise 4.9

Published on 25 Mar 2026 - 1:20

220

Views

Is there a unique way to make $\operatorname{Spec} R$ into an affine scheme?

Published on 09 Apr 2026 - 1:51

68

Views

Tensoring a module with an ideal

Published on 11 Apr 2026 - 5:39

62

Views

Holomorphic function with prescribed orders

Published on 11 Apr 2026 - 11:24

358

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Recover an ultrafilter from a maximal ideal

Published on 31 Mar 2026 - 15:44

65

Views

If $R_P$ is reduced, is there a Zariski basic open set $D(f)$ containing $P$ such that $R_f$ is also reduced?

Published on 25 Mar 2026 - 12:27

567

Views

The "reduction to the affine case" trick [Scheme theory]

Published on 25 Mar 2026 - 14:31

List Question

Does every closed subset of the underlying space of a Noetherian scheme admits a natural closed subscheme structure?

quotient ring which is not local

Direct Limit of Both Rings and Their Modules

About a localization

Showing that $R[x_1,...,x_n]$ is the only $R$-algebra up to isomorphism that satisfies the universal property of the polynomial ring.

Demystify the Hilbert Function

Systematic Way to find System of Parameters of Local Rings

Show that the ideal $((x_1-\alpha_1)^{t_1},...,(x_n-\alpha_n)^{t_n})$ is primary.

Building the Henselization from above: J.S. Milne, Étale Cohomology (PMS-33), Exercise 4.9

Is there a unique way to make $\operatorname{Spec} R$ into an affine scheme?

Tensoring a module with an ideal

Holomorphic function with prescribed orders

Recover an ultrafilter from a maximal ideal

If $R_P$ is reduced, is there a Zariski basic open set $D(f)$ containing $P$ such that $R_f$ is also reduced?

The "reduction to the affine case" trick [Scheme theory]

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