List questions from maximal-and-prime-ideals

Published on 24 Jan 2021 - 10:56

197

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Confusion about the definition of maximal ideal

Published on 31 Mar 2026 - 17:49

100

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$ \mathfrak{m}_{a}=\left\langle X-a^{2}, Y-a^{3}\right\rangle $ is maximal ideal

Published on 26 Jan 2021 - 12:50

240

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Does $x$ irreducible in ring $R$ imply $(x)$ maximal ideal of $R$?

Published on 28 Jan 2021 - 9:28

157

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An affine $K$-algebra factored by a maximal ideal is contained in a finitely generated $K$-domain

Published on 27 Mar 2026 - 2:07

187

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A ring is Jacobson iff $Spec_{max}(R)$ is dense in any closed topological subspace of $Spec(R)$

Published on 26 Mar 2026 - 21:27

333

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Is $I= \langle 5, x^2\rangle$ a principal ideal or not in $\Bbb Z[x]$?

Published on 01 Feb 2021 - 19:12

1.3k

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"Drawing a Picture" of $\operatorname{Spec}(\mathbb{Z})$

Published on 02 Feb 2021 - 0:03

112

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Prove that $a + \langle b \rangle$ is a unit in the quotient ring $R/\langle b \rangle$ if and only if $a$ does not divide $b$ in $R$.

Published on 07 Feb 2021 - 6:32

60

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Is $Z(f(x,y,z))$ affine variety in $\mathbb{A^3}_{\mathbb{R}}$?

Published on 27 Mar 2026 - 5:59

123

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Jacobson radical of unitary subring

Published on 07 Feb 2021 - 20:25

100

Views

Counterexamples to standard assertions on associated primes

Published on 25 Mar 2026 - 16:06

344

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If $R$ is a Noetherian ring and $M$ is a maximal ideal in $R[X]$, is $M \cap R$ a maximal ideal of $R$?

Published on 18 Feb 2021 - 21:51

608

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What are the prime and maximal ideals of the cartesian product of commutative rings?

Published on 18 Feb 2021 - 22:36

52

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$M\subset N$ for $R$-modules $M,N$ if $S_{\mathfrak m}^{-1}M\subset S_{\mathfrak m}^{-1}N$ for all maximal ideals $\mathfrak m\subset R$?

Published on 31 Mar 2026 - 20:07

List Question

Why $M$ is not the zero module?

Confusion about the definition of maximal ideal

$ \mathfrak{m}_{a}=\left\langle X-a^{2}, Y-a^{3}\right\rangle $ is maximal ideal

Does $x$ irreducible in ring $R$ imply $(x)$ maximal ideal of $R$?

An affine $K$-algebra factored by a maximal ideal is contained in a finitely generated $K$-domain

A ring is Jacobson iff $Spec_{max}(R)$ is dense in any closed topological subspace of $Spec(R)$

Is $I= \langle 5, x^2\rangle$ a principal ideal or not in $\Bbb Z[x]$?

"Drawing a Picture" of $\operatorname{Spec}(\mathbb{Z})$

Prove that $a + \langle b \rangle$ is a unit in the quotient ring $R/\langle b \rangle$ if and only if $a$ does not divide $b$ in $R$.

Is $Z(f(x,y,z))$ affine variety in $\mathbb{A^3}_{\mathbb{R}}$?

Jacobson radical of unitary subring

Counterexamples to standard assertions on associated primes

If $R$ is a Noetherian ring and $M$ is a maximal ideal in $R[X]$, is $M \cap R$ a maximal ideal of $R$?

What are the prime and maximal ideals of the cartesian product of commutative rings?

$M\subset N$ for $R$-modules $M,N$ if $S_{\mathfrak m}^{-1}M\subset S_{\mathfrak m}^{-1}N$ for all maximal ideals $\mathfrak m\subset R$?

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