List questions from commutative-algebra

Published on 25 Mar 2026 - 16:01

159

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Let $I = (X,Y) \subset k[X,Y]$ then $\dim_k(k[X,Y]/I^n) = \frac{n(n+1)}{2}$

Published on 22 Mar 2026 - 22:21

266

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Converse of Uniqueness of Universal Property of Tensor Products?

Published on 25 Mar 2026 - 1:20

324

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When is the preimage of a hypersurface a hypersurface

Published on 12 Mar 2018 - 8:20

98

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Ring homomorphism $\mathbb{Z}[[t]]\otimes_\mathbb{Z} \mathbb{Q}\rightarrow \mathbb{Q}[[t]]$

Published on 12 Mar 2018 - 10:06

42

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Can $A[[X]]$ be a finitely generated $A$-algebra?

Published on 25 Mar 2026 - 15:41

129

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Showing that $\mathbb{Z}[\phi]$ is a UFD, where $\phi^2+\phi+1=0$.

Published on 20 Mar 2026 - 4:07

363

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Why $K[x,y]$ and $K[x,y,z]/(xz-y^2)$ are not isomorphic as rings?

Published on 26 Mar 2026 - 22:58

111

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Looking for easy example of 2-dimensional Noetherian domain which is not Cohen-Macaulay

Published on 22 Mar 2026 - 14:07

47

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Trouble understanding proof on primary modules

Published on 12 Mar 2018 - 16:56

128

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Statement of Lech's lemma

Published on 23 Mar 2026 - 7:31

2.5k

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Definition of height of an ideal

Published on 25 Mar 2026 - 16:39

551

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Trying to understand how the Gelfand spectrum relates to the usual notion of spectrum of an operator?

Published on 22 Mar 2026 - 21:52

163

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Do the prime ideals that determine the Krull dimension of a ring have to be proper?

Published on 25 Mar 2026 - 12:35

43

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Maximal Ideals of $R_f$ can be identied with those maximal ideals of R which don’t contain f

Published on 25 Mar 2026 - 17:41

List Question

What happens when localising with a non-prime ideal

Let $I = (X,Y) \subset k[X,Y]$ then $\dim_k(k[X,Y]/I^n) = \frac{n(n+1)}{2}$

Converse of Uniqueness of Universal Property of Tensor Products?

When is the preimage of a hypersurface a hypersurface

Ring homomorphism $\mathbb{Z}[[t]]\otimes_\mathbb{Z} \mathbb{Q}\rightarrow \mathbb{Q}[[t]]$

Can $A[[X]]$ be a finitely generated $A$-algebra?

Showing that $\mathbb{Z}[\phi]$ is a UFD, where $\phi^2+\phi+1=0$.

Why $K[x,y]$ and $K[x,y,z]/(xz-y^2)$ are not isomorphic as rings?

Looking for easy example of 2-dimensional Noetherian domain which is not Cohen-Macaulay

Trouble understanding proof on primary modules

Statement of Lech's lemma

Definition of height of an ideal

Trying to understand how the Gelfand spectrum relates to the usual notion of spectrum of an operator?

Do the prime ideals that determine the Krull dimension of a ring have to be proper?

Maximal Ideals of $R_f$ can be identied with those maximal ideals of R which don’t contain f

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