List questions from commutative-algebra

Published on 14 Apr 2026 - 1:39

91

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Geometric viewpoint on $\Bbbk[t]\to \Bbbk(t)$ not being of finite type

Published on 10 May 2026 - 21:23

897

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Dedekind domain with finite prime ideals is PID (a corollary on Serre's "Local fields" book).

Published on 10 May 2026 - 13:26

683

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Localization of finite direct product of ring at an element

Published on 10 May 2026 - 13:10

154

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Intuitive computation of localizations

Published on 10 May 2026 - 12:31

54

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Anything wrong with this proof?

Published on 14 Apr 2026 - 2:19

64

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If $f = a_0 + a_1t + \cdots\in\mathbb{Z}_p[[t]]$ has $p\mid a_0$ but $p\nmid f$, could $1/f$ have bounded denominators in $\mathbb{Q}_p[[t]]$?

Published on 14 Apr 2026 - 5:11

63

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Is the extension integral?

Published on 09 Apr 2026 - 20:00

130

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Contraction of primes associated to nonzerodivisors

Published on 17 Apr 2026 - 13:57

496

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Faithful modules in integral dependence

Published on 11 Apr 2026 - 7:26

211

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Embedded primes in reduced rings

Published on 10 May 2026 - 14:50

65

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integrally closed subrings of Laurent polynomials

Published on 12 Apr 2026 - 10:36

375

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Prove that $k[X]\simeq k$ using Noether's fundamental theorem (exercise $5.30$ from W. Fulton)

Published on 29 Apr 2026 - 12:55

216

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The complex numbers as a quotient of $\prod_{p\in\mathcal{P}}\bar{\mathbb{F}}_p$

Published on 16 Apr 2026 - 15:58

74

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Quotient of Dedekind rings by a power of a prime ideal

Published on 14 Apr 2026 - 15:37

List Question

completion of Ext

Geometric viewpoint on $\Bbbk[t]\to \Bbbk(t)$ not being of finite type

Dedekind domain with finite prime ideals is PID (a corollary on Serre's "Local fields" book).

Localization of finite direct product of ring at an element

Intuitive computation of localizations

Anything wrong with this proof?

If $f = a_0 + a_1t + \cdots\in\mathbb{Z}_p[[t]]$ has $p\mid a_0$ but $p\nmid f$, could $1/f$ have bounded denominators in $\mathbb{Q}_p[[t]]$?

Is the extension integral?

Contraction of primes associated to nonzerodivisors

Faithful modules in integral dependence

Embedded primes in reduced rings

integrally closed subrings of Laurent polynomials

Prove that $k[X]\simeq k$ using Noether's fundamental theorem (exercise $5.30$ from W. Fulton)

The complex numbers as a quotient of $\prod_{p\in\mathcal{P}}\bar{\mathbb{F}}_p$

Quotient of Dedekind rings by a power of a prime ideal

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