List questions from commutative-algebra

Published on 25 Mar 2026 - 13:56

97

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Two polynomials generating $\mathbb{C}(x,y^2)$

Published on 28 Mar 2026 - 22:24

51

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Showing that the Krull dimension of a certain domain is 1.

Published on 25 Mar 2026 - 3:02

201

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Let $R$ be a Discrete Valuation Ring with unique maximal ideal $M$. Show that $M^n/M^{n+1}$ is a vector space.

Published on 29 Mar 2026 - 4:44

54

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Prove $\mathrm{Ker}(\varphi)=(X^2Z-Y^2,YX^4-Z^2,X^6-YZ)$ over the ring $S=k[X,Y,Z]$ where $k$ is a field.

Published on 09 May 2018 - 12:52

275

Views

Laurent polynomial rings are integrally closed

Published on 09 May 2018 - 13:55

150

Views

Field of fractions generated over a base field

Published on 09 May 2018 - 18:01

50

Views

Showing a property of the zariski topology

Published on 25 Mar 2026 - 11:06

171

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Proving a ring homomorphism for the ring of integers over its ideal

Published on 10 May 2018 - 3:22

161

Views

Hilbert function of an Artinian ideal

Published on 10 May 2018 - 14:39

47

Views

Determining if a quotient of $\Bbb Q[t_1, t_2, \ldots]$ is Noetherian

Published on 10 May 2018 - 16:29

46

Views

Closed subsets in $mSpec C(X, \mathbb{R})$

Published on 10 May 2018 - 18:08

197

Views

$\mathbb{R}[X,Y]/(Y-X^2,Y+X)\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$

Published on 28 Mar 2026 - 10:04

63

Views

Proving an ideal is prime

Published on 11 May 2018 - 7:56

199

Views

Prove the support of a module is Noetherian

Published on 11 May 2018 - 8:39

List Question

Fiber of the sheaf of Relative Differentials (Qing Liu)

Two polynomials generating $\mathbb{C}(x,y^2)$

Showing that the Krull dimension of a certain domain is 1.

Let $R$ be a Discrete Valuation Ring with unique maximal ideal $M$. Show that $M^n/M^{n+1}$ is a vector space.

Prove $\mathrm{Ker}(\varphi)=(X^2Z-Y^2,YX^4-Z^2,X^6-YZ)$ over the ring $S=k[X,Y,Z]$ where $k$ is a field.

Laurent polynomial rings are integrally closed

Field of fractions generated over a base field

Showing a property of the zariski topology

Proving a ring homomorphism for the ring of integers over its ideal

Hilbert function of an Artinian ideal

Determining if a quotient of $\Bbb Q[t_1, t_2, \ldots]$ is Noetherian

Closed subsets in $mSpec C(X, \mathbb{R})$

$\mathbb{R}[X,Y]/(Y-X^2,Y+X)\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$

Proving an ideal is prime

Prove the support of a module is Noetherian

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