List questions from commutative-algebra

Published on 19 Jun 2019 - 23:01

149

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Minimal primary decomposition of ideal in $k[x,y,z]$

Published on 26 Mar 2026 - 10:04

336

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Nakayama's Lemma, Stalks and Fibres (Hartshorne III.12.7.2)

Published on 27 Mar 2026 - 6:12

75

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Free right resolution?

Published on 01 Apr 2026 - 16:05

73

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Does the definition of ideal quotient $(\mathfrak{a}:\mathfrak{b})$ actually require $\mathfrak{b}$ to be an ideal?

Published on 20 Jun 2019 - 22:11

416

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Krull dimension of polynomial ring in one variable

Published on 25 Mar 2026 - 13:54

280

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Intersection of two local rings

Published on 05 Apr 2026 - 22:35

46

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Counterexamples where $\sum_i (a_i : b) \subsetneq (\sum_i a_i :b)$ or where $\sum_i (a: b_i) \subsetneq (a : \bigcap_i b_i)$?

Published on 29 Mar 2026 - 14:59

784

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torsion modules of short exact sequences

Published on 26 Mar 2026 - 4:52

162

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$\operatorname{Spec} k[x_1,...,x_n]/(f(x_1,...,x_n))$ for$ f(x_1,...,x_n)$ irreducible are all homeomorphic?

Published on 09 Apr 2026 - 0:52

31

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Does the $\mathrm{Spec}(F)$ equal $\overline{F}$ for a field $F$?

Published on 31 Mar 2026 - 23:50

425

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Is the Ring of Integers of A Number Field a GCD Domain? The Ring of S-Integers?

Published on 25 Mar 2026 - 17:41

93

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Wikipedia's definition of finitely generated algebra.

Published on 09 Apr 2026 - 7:24

124

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Pairwise Commuting Elements Generating a Certain Subalgebra

Published on 25 Mar 2026 - 18:58

136

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Monic polynomials $f\in R[x]$ with $f-a$ irreducible for almost all values of $a\in R$

Published on 27 Mar 2026 - 5:41

List Question

every irreducible component of $Y \cap H$ has dimension $r-1$

Minimal primary decomposition of ideal in $k[x,y,z]$

Nakayama's Lemma, Stalks and Fibres (Hartshorne III.12.7.2)

Free right resolution?

Does the definition of ideal quotient $(\mathfrak{a}:\mathfrak{b})$ actually require $\mathfrak{b}$ to be an ideal?

Krull dimension of polynomial ring in one variable

Intersection of two local rings

Counterexamples where $\sum_i (a_i : b) \subsetneq (\sum_i a_i :b)$ or where $\sum_i (a: b_i) \subsetneq (a : \bigcap_i b_i)$?

torsion modules of short exact sequences

$\operatorname{Spec} k[x_1,...,x_n]/(f(x_1,...,x_n))$ for$ f(x_1,...,x_n)$ irreducible are all homeomorphic?

Does the $\mathrm{Spec}(F)$ equal $\overline{F}$ for a field $F$?

Is the Ring of Integers of A Number Field a GCD Domain? The Ring of S-Integers?

Wikipedia's definition of finitely generated algebra.

Pairwise Commuting Elements Generating a Certain Subalgebra

Monic polynomials $f\in R[x]$ with $f-a$ irreducible for almost all values of $a\in R$

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