List questions from maximal-and-prime-ideals

Published on 14 Mar 2019 - 22:50

429

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Does this property of comaximal ideals always hold?

Published on 15 Mar 2019 - 2:05

45

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Prime ideal being maximal ideal in an affine algebra

Published on 16 Mar 2019 - 6:02

62

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Commutative ring with finitely many minimal primes

Published on 26 Mar 2026 - 9:40

457

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How to prove that $\mathbb{Z}[X]/g\mathbb{Z}[X]$ is not a field?

Published on 17 Mar 2019 - 23:40

62

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If $\mathfrak{p}$ is a prime such that $M_\mathfrak{p} \neq 0$, then $\mathfrak{p}$ contains an associated prime of $M$

Published on 25 Mar 2026 - 13:57

164

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If $P$ is a prime ideal of $R$ and $X\subseteq P$ then there's a minimal ideal

Published on 21 Mar 2019 - 21:29

25

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$\left \langle x,y\right\rangle\subseteq\mathbb{C}[x,y]$ can be shown as $\bigcup_{i\in I}Q_i$ s.t. $Q_i$ is a prime ideal.

Published on 25 Mar 2026 - 12:49

352

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Prime ideals in multi-variable polynomial rings over $\mathbb{Z}$

Published on 25 Mar 2026 - 12:23

341

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Proving ideal is prime ideal

Published on 26 Mar 2019 - 3:23

232

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Use Zorn's lemma to show that every proper ideal of a ring with unity is contained in some maximal ideal.

Published on 02 Apr 2019 - 5:06

35

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Equivalence between valuations

Published on 24 Mar 2026 - 20:30

210

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In a commutative local Noetherian ring $R$ with maximal ideal $J$, if $J$ is not nilpotent then $R$ is an integral domain.

Published on 25 Mar 2026 - 4:41

359

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Prime ideals of $R[x]$ that intersect $R$ in $P$

Published on 17 Apr 2019 - 22:46

164

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Find zero divisors for polynomials in several variables

Published on 21 Apr 2019 - 12:42

List Question

Find all prime ideals in $\mathbb{Z}/n\mathbb{Z}$ where $n>1$

Does this property of comaximal ideals always hold?

Prime ideal being maximal ideal in an affine algebra

Commutative ring with finitely many minimal primes

How to prove that $\mathbb{Z}[X]/g\mathbb{Z}[X]$ is not a field?

If $\mathfrak{p}$ is a prime such that $M_\mathfrak{p} \neq 0$, then $\mathfrak{p}$ contains an associated prime of $M$

If $P$ is a prime ideal of $R$ and $X\subseteq P$ then there's a minimal ideal

$\left \langle x,y\right\rangle\subseteq\mathbb{C}[x,y]$ can be shown as $\bigcup_{i\in I}Q_i$ s.t. $Q_i$ is a prime ideal.

Prime ideals in multi-variable polynomial rings over $\mathbb{Z}$

Proving ideal is prime ideal

Use Zorn's lemma to show that every proper ideal of a ring with unity is contained in some maximal ideal.

Equivalence between valuations

In a commutative local Noetherian ring $R$ with maximal ideal $J$, if $J$ is not nilpotent then $R$ is an integral domain.

Prime ideals of $R[x]$ that intersect $R$ in $P$

Find zero divisors for polynomials in several variables

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