List questions from commutative-algebra

Published on 27 Mar 2026 - 14:18

89

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checking the functor $\texttt{Nil}_n$ is represented by $(\mathbb{Z}[x]/(x^n), \tau_R)$

Published on 25 Mar 2026 - 6:21

130

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If $0 \to \mathrm{Hom}(M, N') \to \mathrm{Hom}(M, N) \to \mathrm{Hom}(M, N'')$ is exact for all $M$, then $0 \to N' \to N \to N''$ is exact

Published on 25 Mar 2026 - 20:53

87

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Given $p,q \in R$, when $(p,q) \subseteq k[p,q]$?

Published on 30 Mar 2026 - 11:57

509

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On injective module homomorphism $M^m \to M^n$ for a faithful, finitely generated, non-zero module $M$ over a commutative ring

Published on 25 Mar 2026 - 14:27

64

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equality of inverse limits in $R=k[x_1,x_2,...]$

Published on 25 Mar 2026 - 8:09

116

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defining functor $Ord$

Published on 02 Apr 2026 - 6:59

637

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What will be the smallest ring containing two rings?

Published on 25 Mar 2026 - 4:36

207

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Are unique prime ideal factorization domains noetherian?

Published on 25 Mar 2026 - 4:38

377

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When is a map of local rings finite?

Published on 27 Mar 2026 - 5:42

51

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Example of a field of functions containing ln(x)

Published on 30 Mar 2026 - 8:01

164

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why separable algebra is a generalisation of separable field extension?

Published on 04 Apr 2026 - 7:52

81

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Are unique prime ideal factorization domains locally noetherian?

Published on 25 Mar 2026 - 6:02

321

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Understanding a proof: Artinian ring implies semilocal

Published on 05 Jan 2019 - 19:58

103

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Exercise 3.30 from Görtz-Wedhorn: local affine algebras

Published on 05 Jan 2019 - 20:42

List Question

Unique prime ideal factorization in domains?

checking the functor $\texttt{Nil}_n$ is represented by $(\mathbb{Z}[x]/(x^n), \tau_R)$

If $0 \to \mathrm{Hom}(M, N') \to \mathrm{Hom}(M, N) \to \mathrm{Hom}(M, N'')$ is exact for all $M$, then $0 \to N' \to N \to N''$ is exact

Given $p,q \in R$, when $(p,q) \subseteq k[p,q]$?

On injective module homomorphism $M^m \to M^n$ for a faithful, finitely generated, non-zero module $M$ over a commutative ring

equality of inverse limits in $R=k[x_1,x_2,...]$

defining functor $Ord$

What will be the smallest ring containing two rings?

Are unique prime ideal factorization domains noetherian?

When is a map of local rings finite?

Example of a field of functions containing ln(x)

why separable algebra is a generalisation of separable field extension?

Are unique prime ideal factorization domains locally noetherian?

Understanding a proof: Artinian ring implies semilocal

Exercise 3.30 from Görtz-Wedhorn: local affine algebras

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