List questions from commutative-algebra

Published on 14 Apr 2026 - 21:02

187

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Prime radical that is nil but not nilpotent

Published on 13 Apr 2026 - 11:36

3.2k

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Quotient of polynomials, PID but not Euclidean domain?

Published on 13 Apr 2026 - 21:45

78

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$\mathbb{Q}[x,1/x]$ is normal?

Published on 16 Apr 2026 - 21:50

157

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Automorphism of certain f.g. free modules

Published on 16 Apr 2026 - 11:59

38

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Do lattices in a field of fractions contain an ideal?

Published on 10 Apr 2026 - 19:54

68

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Two points in a proof of regularity of $R/I$

Published on 11 Apr 2026 - 5:47

4.1k

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Prove that the normalisation of $A=k[X,Y]/(Y^2-X^2-X^3)$ is $k[t]$ where $t=Y/X$ (Reid, Exercise 4.5)

Published on 17 Apr 2026 - 9:50

760

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Is the unique morphism from the empty scheme $\operatorname{Spec}((0))$ to some other scheme $X$ smooth?

Published on 14 Apr 2026 - 4:45

46

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Congruence in localization of rings

Published on 11 Apr 2026 - 13:50

84

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Localizations of $ \mathbb{Z}_{p^k}$

Published on 11 Apr 2026 - 9:44

899

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The geometric interpretation for extension of ideals?

Published on 09 Apr 2026 - 17:55

232

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What is $\operatorname{Ass}\operatorname{Ext}^i(M,N)$?

Published on 16 Apr 2026 - 9:15

162

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$k[X,Y]/(f)$ not finitely generated as a module (Exercise 4.10 Reid, UCA)

Published on 15 Apr 2026 - 17:23

96

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$R^{(I)} \cong K \oplus H$ where $R^{(I)}$ is free but $K$ is not free

Published on 12 Apr 2026 - 8:03

List Question

Basis for the completion of a free module

Prime radical that is nil but not nilpotent

Quotient of polynomials, PID but not Euclidean domain?

$\mathbb{Q}[x,1/x]$ is normal?

Automorphism of certain f.g. free modules

Do lattices in a field of fractions contain an ideal?

Two points in a proof of regularity of $R/I$

Prove that the normalisation of $A=k[X,Y]/(Y^2-X^2-X^3)$ is $k[t]$ where $t=Y/X$ (Reid, Exercise 4.5)

Is the unique morphism from the empty scheme $\operatorname{Spec}((0))$ to some other scheme $X$ smooth?

Congruence in localization of rings

Localizations of $ \mathbb{Z}_{p^k}$

The geometric interpretation for extension of ideals?

What is $\operatorname{Ass}\operatorname{Ext}^i(M,N)$?

$k[X,Y]/(f)$ not finitely generated as a module (Exercise 4.10 Reid, UCA)

$R^{(I)} \cong K \oplus H$ where $R^{(I)}$ is free but $K$ is not free

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