List questions from commutative-algebra

Published on 11 Apr 2026 - 12:58

38

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Is $\left<ad-bc,a+d\right>\subseteq k[a,b,c,d]$ a reduced ideal, and if yes, why?

Published on 15 Apr 2026 - 22:42

214

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Flatness of $A=F[x_1,\dots,x_n]/\langle f_1,\dots,f_k \rangle$

Published on 26 Mar 2026 - 1:04

112

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$(X)$ faithful flat $k[X,Y]$-module

Published on 16 Apr 2026 - 23:52

99

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Flatness of $\frac{A[b]}{\langle u,v \rangle}$ over $A$ and flatness of $\frac{A[w]}{\langle u \rangle}$ over $A$

Published on 26 Mar 2026 - 1:04

161

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Duality for zero-dimensional local Gorenstein algebras

Published on 11 Apr 2026 - 0:11

222

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A good introductory book about differential calculus on commutative algebras?

Published on 13 Apr 2026 - 14:04

82

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Flatness of $\frac{R[T]}{I}$ over $R$ implies that $I$ is principal or $I=R[T]$?

Published on 16 Apr 2026 - 18:06

106

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Direct limit of the finite product of vector spaces

Published on 24 Apr 2026 - 13:03

81

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Matrix over commutative ring with noncommutative diagonal perturbation

Published on 14 Apr 2026 - 0:54

208

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Element of a ring acting as a permutation on an ideal

Published on 25 Mar 2026 - 4:39

66

Views

On the unique factorisation of $R[x_1,y_1,...,x_n,y_n]/(x_1y_1+...+x_ny_n)$ where $R$ is UFD

Published on 16 Apr 2026 - 20:42

1k

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Nice exercises on Hilbert's basis theorem

Published on 15 Apr 2026 - 8:06

88

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Local ring of product of affine varieties at a point

Published on 15 Apr 2026 - 15:26

253

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To show a localisation is a DVR

Published on 27 Mar 2026 - 18:48

List Question

Bogus proof that every ideal in a Dedekind domain is principal

Is $\left<ad-bc,a+d\right>\subseteq k[a,b,c,d]$ a reduced ideal, and if yes, why?

Flatness of $A=F[x_1,\dots,x_n]/\langle f_1,\dots,f_k \rangle$

$(X)$ faithful flat $k[X,Y]$-module

Flatness of $\frac{A[b]}{\langle u,v \rangle}$ over $A$ and flatness of $\frac{A[w]}{\langle u \rangle}$ over $A$

Duality for zero-dimensional local Gorenstein algebras

A good introductory book about differential calculus on commutative algebras?

Flatness of $\frac{R[T]}{I}$ over $R$ implies that $I$ is principal or $I=R[T]$?

Direct limit of the finite product of vector spaces

Matrix over commutative ring with noncommutative diagonal perturbation

Element of a ring acting as a permutation on an ideal

On the unique factorisation of $R[x_1,y_1,...,x_n,y_n]/(x_1y_1+...+x_ny_n)$ where $R$ is UFD

Nice exercises on Hilbert's basis theorem

Local ring of product of affine varieties at a point

To show a localisation is a DVR

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