List questions from maximal-and-prime-ideals

Published on 24 Jul 2012 - 9:38

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Show that any prime ideal from such a ring is maximal.

Published on 11 Oct 2012 - 7:06

507

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Intersecting maximal ideals of $k[x_1,\dots,x_n]$ with $k[x_i]$

Published on 11 Oct 2012 - 22:22

257

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The ideal $(X,Y)$ is prime in $\mathbb{C}[X,Y]$. But is it also maximal?

Published on 28 Mar 2026 - 22:31

243

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The set of prime ideals in the set of ideals $\mathrm{rad}(\mathfrak a:x)$ equals the set of prime ideals in the set of ideals $(\mathfrak a:x)$?

Published on 24 Oct 2012 - 17:30

4.3k

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Prove that prime ideals of a finite ring are maximal

Published on 24 Feb 2026 - 0:30

145

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A question about prime ideals: If $p=a \cap b$ then $p=a$ or $p=b$?

Published on 16 Feb 2013 - 5:04

374

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Show that the ideal of $k[X_1, X_2, X_3]$ generated by $X_1^3-X_3$ and $X_2^2-X_3$ is a prime ideal.

Published on 18 Feb 2013 - 21:57

3.9k

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Maximal ideals in polynomial rings

Published on 26 Feb 2013 - 8:07

2.7k

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Is $(xy-1)$ a maximal ideal in $\mathbb C[x,y]$?

Published on 07 Mar 2013 - 18:17

2.3k

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Number of prime ideals of a ring

Published on 15 Mar 2013 - 10:35

49

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A question about whether an ideal is maximal or not

Published on 31 Jul 2020 - 14:46

508

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Is the finite intersection of prime ideals radical?

Published on 01 Aug 2020 - 22:38

75

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Is the ideal generated by $y$ and $x^2+yx+1$ in $Z[x, y]$ a prime ideal?

Published on 02 Aug 2020 - 12:32

719

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prove $\left(3, 1+\sqrt{-5}\right)$ is prime ideal of $\mathbb{Z}\left[\sqrt{-5}\right]$

Published on 05 Aug 2020 - 12:34

List Question

Classification of prime ideals of $\mathbb{Z}[X]$

Show that any prime ideal from such a ring is maximal.

Intersecting maximal ideals of $k[x_1,\dots,x_n]$ with $k[x_i]$

The ideal $(X,Y)$ is prime in $\mathbb{C}[X,Y]$. But is it also maximal?

The set of prime ideals in the set of ideals $\mathrm{rad}(\mathfrak a:x)$ equals the set of prime ideals in the set of ideals $(\mathfrak a:x)$?

Prove that prime ideals of a finite ring are maximal

A question about prime ideals: If $p=a \cap b$ then $p=a$ or $p=b$?

Show that the ideal of $k[X_1, X_2, X_3]$ generated by $X_1^3-X_3$ and $X_2^2-X_3$ is a prime ideal.

Maximal ideals in polynomial rings

Is $(xy-1)$ a maximal ideal in $\mathbb C[x,y]$?

Number of prime ideals of a ring

A question about whether an ideal is maximal or not

Is the finite intersection of prime ideals radical?

Is the ideal generated by $y$ and $x^2+yx+1$ in $Z[x, y]$ a prime ideal?

prove $\left(3, 1+\sqrt{-5}\right)$ is prime ideal of $\mathbb{Z}\left[\sqrt{-5}\right]$

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