List questions from maximal-and-prime-ideals

Published on 17 Dec 2014 - 6:39

314

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Solution verification: proving that $2$ is not prime in $\mathbb{Z}[\sqrt{-3}]$

Published on 29 Mar 2026 - 4:48

2.5k

Views

Prove that an ideal is not maximal

Published on 20 Dec 2014 - 14:08

959

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Height and coheight of an ideal

Published on 22 Dec 2014 - 6:59

537

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Prove that for all $x \in R$, the ideal $xR$ is proper.

Published on 25 Dec 2014 - 6:15

257

Views

Negative degree valuation: valuation ring and its maximal ideal

Published on 26 Mar 2026 - 4:30

2.2k

Views

Is the complement of a prime ideal closed under both addition and multiplication?

Published on 02 Jan 2015 - 13:43

839

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How to prove that a maximal ideal of a ring is unique?

Published on 03 Oct 2019 - 1:26

204

Views

Maximal ideal of $\mathbb{Z}_{n}[x]$ if $n$ is composite

Published on 27 Feb 2026 - 17:46

36

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Prime ideals in Quotientring

Published on 06 Oct 2019 - 10:10

42

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Show that $K $ is prime ideal of $K $

Published on 06 Oct 2019 - 14:37

878

Views

Irreducible element of $\mathbb{Z}[\sqrt{-d}]$ generating an ideal that isn't prime

Published on 07 Oct 2019 - 18:22

34

Views

Show that $(A-\mathfrak{p})^{-1}B$ is semi local for number ring extension $A\subset B$

Published on 27 Mar 2026 - 14:02

68

Views

Prove that $(z-x^3,y-x^2)$ is a prime ideal

Published on 11 Oct 2019 - 10:17

33

Views

Bijection $\varphi:k^2\tilde{\to}$SpecMax($k[x,y])$

Published on 11 Oct 2019 - 15:10

List Question

Alternative proof of '$I$ is maximal iff $R/I$ is a field'

Solution verification: proving that $2$ is not prime in $\mathbb{Z}[\sqrt{-3}]$

Prove that an ideal is not maximal

Height and coheight of an ideal

Prove that for all $x \in R$, the ideal $xR$ is proper.

Negative degree valuation: valuation ring and its maximal ideal

Is the complement of a prime ideal closed under both addition and multiplication?

How to prove that a maximal ideal of a ring is unique?

Maximal ideal of $\mathbb{Z}_{n}[x]$ if $n$ is composite

Prime ideals in Quotientring

Show that $K $ is prime ideal of $K $

Irreducible element of $\mathbb{Z}[\sqrt{-d}]$ generating an ideal that isn't prime

Show that $(A-\mathfrak{p})^{-1}B$ is semi local for number ring extension $A\subset B$

Prove that $(z-x^3,y-x^2)$ is a prime ideal

Bijection $\varphi:k^2\tilde{\to}$SpecMax($k[x,y])$

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