List questions from maximal-and-prime-ideals

Published on 22 Mar 2026 - 6:36

84

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Proving maximal ideals of $\mathbb{Z}[x]$ contain a prime

Published on 25 Mar 2026 - 15:17

43

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Why is it that $\exists f_1,f_2\in M[f_1, f_2$ have no common factor]?

Published on 25 Mar 2026 - 4:43

466

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Finiteness of prime ideals in Dedekind domains

Published on 25 Mar 2026 - 7:09

765

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What are the prime and maximal ideals of the power set of $\Bbb N$, i.e. $\mathcal P(\Bbb N)$

Published on 11 Mar 2018 - 9:02

2.5k

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Definition of height of an ideal

Published on 21 Mar 2026 - 23:45

851

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Is there an example of a power of prime ideal in a polynomial ring that is not primary?

Published on 17 Mar 2018 - 6:08

150

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Polynomial ring as a finite algebra over a subring

Published on 17 Mar 2018 - 9:24

279

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On the annihilator of a certain quotient module

Published on 18 Mar 2018 - 17:03

196

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Algebraic characterization for the set of all maximal ideals, as a subspace of $\operatorname{Spec} (R)$, to be connected

Published on 25 Mar 2026 - 6:15

351

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Show that $\langle X\rangle$ is the unique maximal ideal of $F[[X]]$.

Published on 24 Mar 2018 - 5:56

117

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If $I\subset \mathbb{Z}[X]$ prime ideal, then $I\cap \mathbb{Z}$ prime ideal in $\mathbb{Z}$

Published on 29 Mar 2018 - 8:50

1.2k

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Show that, the ideal $M_2(2\mathbb{Z})$ is maximal ideal of $M_2(\mathbb{Z})$

Published on 01 Apr 2018 - 6:48

184

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Are non-coprime ideals always contained in some prime ideal?

Published on 03 Apr 2018 - 17:47

45

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Is there an ideal of $(C^0(\mathbb{R}),+,\cdot)$ that isn't prime?

Published on 04 Apr 2018 - 14:04

List Question

Equivalent definitions of associated primes

Proving maximal ideals of $\mathbb{Z}[x]$ contain a prime

Why is it that $\exists f_1,f_2\in M[f_1, f_2$ have no common factor]?

Finiteness of prime ideals in Dedekind domains

What are the prime and maximal ideals of the power set of $\Bbb N$, i.e. $\mathcal P(\Bbb N)$

Definition of height of an ideal

Is there an example of a power of prime ideal in a polynomial ring that is not primary?

Polynomial ring as a finite algebra over a subring

On the annihilator of a certain quotient module

Algebraic characterization for the set of all maximal ideals, as a subspace of $\operatorname{Spec} (R)$, to be connected

Show that $\langle X\rangle$ is the unique maximal ideal of $F[[X]]$.

If $I\subset \mathbb{Z}[X]$ prime ideal, then $I\cap \mathbb{Z}$ prime ideal in $\mathbb{Z}$

Show that, the ideal $M_2(2\mathbb{Z})$ is maximal ideal of $M_2(\mathbb{Z})$

Are non-coprime ideals always contained in some prime ideal?

Is there an ideal of $(C^0(\mathbb{R}),+,\cdot)$ that isn't prime?

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