List questions from ideals

Published on 11 Apr 2026 - 4:42

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$V$ is irreducible exactly then when $I(V )$ is a prime ideal

Published on 02 Apr 2026 - 18:40

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Given a radical ideal, prove that the ideal cannot be prime

Published on 11 Apr 2026 - 18:02

102

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Proof check: find all Prime ideals of $R[T]/\langle x^n\rangle$,

Published on 02 Apr 2026 - 20:32

174

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The finitely generated-ness of ideals $I +rR$ and $I:r$ imply $I$ is a finitely generated ideal

Published on 28 Mar 2026 - 6:59

694

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Preimage of prime ideal under induced map

Published on 02 Apr 2026 - 20:38

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if R is a commutative ring in which all the prime ideals are finitely generated then R is Noetherian

Published on 02 Feb 2015 - 12:38

83

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If there exists a vertex of $ \Gamma_{2}(R)\setminus J(R) $ which is adjacent to every other vertex then $ R \cong \mathbb{Z}_{2}\times F$

Published on 05 Feb 2015 - 16:39

117

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Chain of ideals in nilpotent algebra

Published on 10 Apr 2026 - 20:40

124

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Describe $\mathbb{Z}[\omega] / (2)$

Published on 09 Apr 2026 - 3:04

173

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Frobenius powers of an ideal does not depend on the choice of a system of generators

Published on 08 Apr 2026 - 17:40

166

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Question on prime ideals of ${\mathbb Z}[x]$

Published on 10 Apr 2026 - 2:57

575

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Prove that for ideals I and J of a commutative ring, $√(I∩J)=√(IJ)$

Published on 09 Feb 2015 - 8:52

255

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Show that $Z(XY,XZ,YZ)$ is not irreducible

Published on 09 Feb 2015 - 9:45

999

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Let K be a field, and $I=(XY,(X-Y)Z)⊆K[X,Y,Z]$. Prove that $√I=(XY,XZ,YZ)$.

Published on 09 Feb 2015 - 10:39

List Question

Can we use the Nullstellensatz?

$V$ is irreducible exactly then when $I(V )$ is a prime ideal

Given a radical ideal, prove that the ideal cannot be prime

Proof check: find all Prime ideals of $R[T]/\langle x^n\rangle$,

The finitely generated-ness of ideals $I +rR$ and $I:r$ imply $I$ is a finitely generated ideal

Preimage of prime ideal under induced map

if R is a commutative ring in which all the prime ideals are finitely generated then R is Noetherian

If there exists a vertex of $ \Gamma_{2}(R)\setminus J(R) $ which is adjacent to every other vertex then $ R \cong \mathbb{Z}_{2}\times F$

Chain of ideals in nilpotent algebra

Describe $\mathbb{Z}[\omega] / (2)$

Frobenius powers of an ideal does not depend on the choice of a system of generators

Question on prime ideals of ${\mathbb Z}[x]$

Prove that for ideals I and J of a commutative ring, $√(I∩J)=√(IJ)$

Show that $Z(XY,XZ,YZ)$ is not irreducible

Let K be a field, and $I=(XY,(X-Y)Z)⊆K[X,Y,Z]$. Prove that $√I=(XY,XZ,YZ)$.

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