List questions from maximal-and-prime-ideals

Published on 25 Mar 2026 - 13:56

110

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Suppose $R$ is an integral domain and $p$ is a prime ideal

Published on 02 Jul 2019 - 20:28

172

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Show that the ideal $((x_1-\alpha_1)^{t_1},...,(x_n-\alpha_n)^{t_n})$ is primary.

Published on 25 Mar 2026 - 23:09

168

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Commutative unitary ring without maximal ideal without axiom of choice

Published on 07 Jul 2019 - 13:54

145

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Which are the possible maximal ideals in $C[0,1]$ containing a prime which is not maximal?

Published on 11 Jul 2019 - 5:19

333

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Prove that $\sqrt{I} = \sqrt{J} \Leftrightarrow V(I) = V(J)$

Published on 11 Jul 2019 - 5:32

100

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$0 \subset (x_1 - a_1) \subset (x_1 - a_1, x_2-a_2) \subset ... \subset (x_1-a_1,..., x_n - a_n)$ is a (strictly) ascending chain of prime ideals

Published on 25 Mar 2026 - 20:12

106

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Image of the complement of an ideal - when $\phi\left(R\setminus I\right)=\phi\left(I\right)\setminus \phi\left(I\right)$?

Published on 15 Jul 2019 - 22:37

615

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A prime ideal of a polynomial ring

Published on 16 Jul 2019 - 5:46

684

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Associated primes in a reduced ring

Published on 16 Jul 2019 - 18:54

648

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A variety $X$ is irreducible $\iff I(X)$ is prime

Published on 25 Mar 2026 - 14:34

64

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quotient ring of the class $C^{\infty}$ functions on $\mathbb{R}$

Published on 25 Mar 2026 - 23:37

1.6k

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maximal ideals of $C((0,1))$

Published on 22 Jul 2019 - 19:45

395

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How can we prove the existence of algebraic closures from first-order compactness?

Published on 27 Mar 2026 - 17:57

553

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Maximal ideal and not algebraically closed field

Published on 25 Mar 2026 - 4:38

List Question

Number of maximal ideals of $F_q[x_1,...,x_n]$

Suppose $R$ is an integral domain and $p$ is a prime ideal

Show that the ideal $((x_1-\alpha_1)^{t_1},...,(x_n-\alpha_n)^{t_n})$ is primary.

Commutative unitary ring without maximal ideal without axiom of choice

Which are the possible maximal ideals in $C[0,1]$ containing a prime which is not maximal?

Prove that $\sqrt{I} = \sqrt{J} \Leftrightarrow V(I) = V(J)$

$0 \subset (x_1 - a_1) \subset (x_1 - a_1, x_2-a_2) \subset ... \subset (x_1-a_1,..., x_n - a_n)$ is a (strictly) ascending chain of prime ideals

Image of the complement of an ideal - when $\phi\left(R\setminus I\right)=\phi\left(I\right)\setminus \phi\left(I\right)$?

A prime ideal of a polynomial ring

Associated primes in a reduced ring

A variety $X$ is irreducible $\iff I(X)$ is prime

quotient ring of the class $C^{\infty}$ functions on $\mathbb{R}$

maximal ideals of $C((0,1))$

How can we prove the existence of algebraic closures from first-order compactness?

Maximal ideal and not algebraically closed field

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