List questions from commutative-algebra

168

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Localization Question: $\frac{a}{b}\in\left(\mathbb{Z}_{(p)}\right)^{\times}\iff\frac{b}{a}\in\mathbb{Z}_{(p)}$

Published on 16 Apr 2026 - 12:37

2.2k

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Irreducible components of affine variety

Published on 15 Apr 2026 - 21:12

406

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Does any (noetherian) integral domain have a "UFD closure"?

Published on 14 Apr 2026 - 20:41

733

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Show that $Rad(I)$ is a prime ideal

Published on 14 Apr 2026 - 7:20

50

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$\overline{V(I)-V(J)}=V(\bigcup_{n=1}^{\infty}I\colon J^n)$

Published on 15 Apr 2026 - 0:32

615

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Extension of R-linear derivation to localization

Published on 13 Apr 2026 - 6:24

95

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Flatness on the affine line for a coherent sheaf

Published on 15 Apr 2026 - 21:16

74

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Is an ideal prime when its complex extension is prime?

Published on 10 Apr 2026 - 23:09

1.6k

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Ambiguity in the definition of unmixed ideal

Published on 12 Apr 2026 - 6:50

300

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Associated non-minimal prime ideal

Published on 16 Apr 2026 - 4:32

953

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$A$ is a commutative ring, $P$ is a prime ideal. Prove $A_P$ is local ring

Published on 15 Apr 2026 - 18:45

489

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Counterexample in Dedekind domains

Published on 14 Apr 2026 - 10:16

108

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construction of $S^{-1}A$

Published on 14 Apr 2026 - 23:29

196

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$k[t^{a_1},t^{a_2},t^{a_3}]$ in the form $k[x,y,z]/(...)$

Published on 17 Apr 2026 - 14:19

1.2k

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Prime ideals in $A$ and prime ideals in $S^{-1}A$

Published on 14 Apr 2026 - 19:21

List Question

Localization Question: $\frac{a}{b}\in\left(\mathbb{Z}_{(p)}\right)^{\times}\iff\frac{b}{a}\in\mathbb{Z}_{(p)}$

Irreducible components of affine variety

Does any (noetherian) integral domain have a "UFD closure"?

Show that $Rad(I)$ is a prime ideal

$\overline{V(I)-V(J)}=V(\bigcup_{n=1}^{\infty}I\colon J^n)$

Extension of R-linear derivation to localization

Flatness on the affine line for a coherent sheaf

Is an ideal prime when its complex extension is prime?

Ambiguity in the definition of unmixed ideal

Associated non-minimal prime ideal

$A$ is a commutative ring, $P$ is a prime ideal. Prove $A_P$ is local ring

Counterexample in Dedekind domains

construction of $S^{-1}A$

$k[t^{a_1},t^{a_2},t^{a_3}]$ in the form $k[x,y,z]/(...)$

Prime ideals in $A$ and prime ideals in $S^{-1}A$

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