List questions from maximal-and-prime-ideals

Published on 26 May 2019 - 3:05

809

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Ideals of $R[x]/I[x]$, where $I$ is a maximal ideal of $R$

Published on 27 May 2019 - 15:57

73

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If $g(X)\in \Bbb Z[X]$ irreducible polynomial, then $\langle g(X) \rangle \trianglelefteq \Bbb Z[X]$ is not maximal

Published on 28 May 2019 - 14:10

242

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Nonzero prime ideal containing no other nonzero prime ideal

Published on 25 Mar 2026 - 10:53

33

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If $\mathbb Z_{15} / P \cong \mathbb Z_{3}$, then prove that $\mathbb Z{_{15}}_{P} \cong \mathbb Z_{3}$

Published on 09 Jun 2019 - 12:16

96

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Maximal Ideal Criteria in a Non-Commutative case

Published on 12 Jun 2019 - 1:48

194

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Converse of : If $M$ is Noetherian then $M_m$ is Noetherian for every $m\in\operatorname{Max}(R)$.

Published on 25 Mar 2026 - 15:42

263

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Dummit and Foote $(3^{ed})$ 7.4.13

Published on 14 Jun 2019 - 4:51

207

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Can intersection of two different maximal ideals of Euclidean ring contain prime element?

Published on 15 Jun 2019 - 16:26

207

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Prove that $u-i$ is a maximal ideal of $\frac {\Bbb C[X,Y]} {\left (X^2+Y^2-1 \right )}.$

Published on 16 Jun 2019 - 6:49

493

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Find an ideal $I$ in $A$ so that $A/I$ is a finite field with $25$ elements.

Published on 25 Mar 2026 - 12:27

153

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Short Question: $(p)$ for a prime is not a maximal ideal in $\mathbb{Z}[X]$

Published on 20 Jun 2019 - 15:46

654

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On the maximal ideals of $\Bbb Z_5[X,Y]$ which contain $\langle Y \rangle$

Published on 21 Jun 2019 - 14:50

483

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Problem 1.23 in Fulton's Algebraic curves

Published on 23 Jun 2019 - 11:32

156

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Proper ideals of local rings

Published on 25 Mar 2026 - 6:02

List Question

The maximal ideals of $\Bbb Z[X]$

Ideals of $R[x]/I[x]$, where $I$ is a maximal ideal of $R$

If $g(X)\in \Bbb Z[X]$ irreducible polynomial, then $\langle g(X) \rangle \trianglelefteq \Bbb Z[X]$ is not maximal

Nonzero prime ideal containing no other nonzero prime ideal

If $\mathbb Z_{15} / P \cong \mathbb Z_{3}$, then prove that $\mathbb Z{_{15}}_{P} \cong \mathbb Z_{3}$

Maximal Ideal Criteria in a Non-Commutative case

Converse of : If $M$ is Noetherian then $M_m$ is Noetherian for every $m\in\operatorname{Max}(R)$.

Dummit and Foote $(3^{ed})$ 7.4.13

Can intersection of two different maximal ideals of Euclidean ring contain prime element?

Prove that $u-i$ is a maximal ideal of $\frac {\Bbb C[X,Y]} {\left (X^2+Y^2-1 \right )}.$

Find an ideal $I$ in $A$ so that $A/I$ is a finite field with $25$ elements.

Short Question: $(p)$ for a prime is not a maximal ideal in $\mathbb{Z}[X]$

On the maximal ideals of $\Bbb Z_5[X,Y]$ which contain $\langle Y \rangle$

Problem 1.23 in Fulton's Algebraic curves

Proper ideals of local rings

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