List questions from commutative-algebra

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Homomorphism and modules

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No local normalization

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Minimal prime ideals and zero-divisors.

Published on 27 Apr 2018 - 1:35

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Motivation behind Primary Decomposition

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Looking for a reference for this proof of radical ideals being finite intersections of prime ideals

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If $f$ is injective, $\alpha^{e} \subseteq \beta^{e}$, then is it true $\alpha\subseteq \beta$?

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Finiteness of integral closure.

Published on 27 Apr 2018 - 18:44

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Is $ \mathbb{R}[x,y]/(x^2-y^2) \cong \mathbb{R}[x,y]/(x-y) \times \mathbb{R}[x,y]/(x+y) $?

Published on 26 Mar 2026 - 2:47

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If $A^{\wedge}$ is the completion of a local ring, do we always have $\mathfrak{m}^{\wedge}=\mathfrak{m}A^{\wedge}$?

Published on 28 Apr 2018 - 10:29

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Example of coherent ring with finite self FP-Injective dimension

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Tensor product of noetherian modules is also noetherian?

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The Jacobson radical of polynomial ring

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194

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Localization of infinite variable ring over a prime ideal is not Noetherian

Published on 29 Apr 2018 - 14:45

244

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A decomposition on the roots of unity

Published on 27 Mar 2026 - 9:29

List Question

Example of an invertible ideal which contains a zero divisor as one of its generators

Homomorphism and modules

No local normalization

Minimal prime ideals and zero-divisors.

Motivation behind Primary Decomposition

Looking for a reference for this proof of radical ideals being finite intersections of prime ideals

If $f$ is injective, $\alpha^{e} \subseteq \beta^{e}$, then is it true $\alpha\subseteq \beta$?

Finiteness of integral closure.

Is $ \mathbb{R}[x,y]/(x^2-y^2) \cong \mathbb{R}[x,y]/(x-y) \times \mathbb{R}[x,y]/(x+y) $?

If $A^{\wedge}$ is the completion of a local ring, do we always have $\mathfrak{m}^{\wedge}=\mathfrak{m}A^{\wedge}$?

Example of coherent ring with finite self FP-Injective dimension

Tensor product of noetherian modules is also noetherian?

The Jacobson radical of polynomial ring

Localization of infinite variable ring over a prime ideal is not Noetherian

A decomposition on the roots of unity

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