Question

Show that $\langle 13 \rangle$ is a prime ideal in $\mathbb{Z[\sqrt{-5}]}$

score 1.6k · Answer 1 · 2026-04-12 01:08:52

1.6k

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Show that $\langle 13 \rangle$ is a prime ideal in $\mathbb{Z[\sqrt{-5}]}$

Published on 12 Apr 2026 - 1:08

score 58 · Answer 2 · 2015-02-26 16:41:18

58

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The ideals of $A \times B$ for fields $A,B$.are principal

Published on 26 Feb 2015 - 16:41

score 135 · Answer 3 · 2026-04-08 20:33:54

135

Views

A proof about prime ideals

Published on 08 Apr 2026 - 20:33

score 311 · Answer 4 · 2015-02-26 21:46:07

311

Views

Show that a collection of functions $I$ is an ideal

Published on 26 Feb 2015 - 21:46

score 549 · Answer 5 · 2026-04-11 19:08:01

549

Views

Ideal of $\mathbb{C}[X,Y]$ contained in infinitely many distinct proper ideals

Published on 11 Apr 2026 - 19:08

score 70 · Answer 6 · 2026-04-11 03:53:20

70

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Inclusion of fractional ideals implies equality

Published on 11 Apr 2026 - 3:53

score 1.8k · Answer 7 · 2026-04-11 18:18:47

1.8k

Views

Showing that if the initial ideal of I is radical, then I is radical.

Published on 11 Apr 2026 - 18:18

score 394 · Answer 8 · 2015-03-02 01:22:16

394

Views

How to show that $J$ is a left ideal of $R$?

Published on 02 Mar 2015 - 1:22

score 833 · Answer 9 · 2026-04-09 15:05:24

833

Views

Chinese Remainder Theorem proof using maximal ideals

Published on 09 Apr 2026 - 15:05

score 463 · Answer 10 · 2026-03-29 20:56:36

463

Views

The rings Z[$\sqrt{6}$] and Z[$\sqrt{7}$] are PIDs. Exhibit generators for their ideals (3,$\sqrt{6}$), (5, 4 + $\sqrt{6}$), (2, 1 + $\sqrt{7}$)

Published on 29 Mar 2026 - 20:56

score 1.1k · Answer 11 · 2015-03-03 00:09:11

1.1k

Views

Prove the Ring Homomorphism is Surjective

Published on 03 Mar 2015 - 0:09

score 61 · Answer 12 · 2015-03-03 11:54:16

61

Views

Relation between Variety of $(I\cap J)$ and Variety of $(I)$ $\cap$ Variety of $(J)$

Published on 03 Mar 2015 - 11:54

score 60 · Answer 13 · 2026-04-06 13:49:19

60

Views

Want to show that $g\in I$ where $I$ is an ideal, given the following conditions

Published on 06 Apr 2026 - 13:49

score 451 · Answer 14 · 2026-03-25 11:03:40

451

Views

Finding a finite generating set of an ideal of monomials

Published on 25 Mar 2026 - 11:03

score 169 · Answer 15 · 2015-03-03 15:36:42

169

Views

If $I$ is a proper ideal of $C[0,1]$ , then should there exist $a \in [0,1]$ such that $f(a)=0 , \forall f \in I$?

Published on 03 Mar 2015 - 15:36

List Question

Show that $\langle 13 \rangle$ is a prime ideal in $\mathbb{Z[\sqrt{-5}]}$

The ideals of $A \times B$ for fields $A,B$.are principal

A proof about prime ideals

Show that a collection of functions $I$ is an ideal

Ideal of $\mathbb{C}[X,Y]$ contained in infinitely many distinct proper ideals

Inclusion of fractional ideals implies equality

Showing that if the initial ideal of I is radical, then I is radical.

How to show that $J$ is a left ideal of $R$?

Chinese Remainder Theorem proof using maximal ideals

The rings Z[$\sqrt{6}$] and Z[$\sqrt{7}$] are PIDs. Exhibit generators for their ideals (3,$\sqrt{6}$), (5, 4 + $\sqrt{6}$), (2, 1 + $\sqrt{7}$)

Prove the Ring Homomorphism is Surjective

Relation between Variety of $(I\cap J)$ and Variety of $(I)$ $\cap$ Variety of $(J)$

Want to show that $g\in I$ where $I$ is an ideal, given the following conditions

Finding a finite generating set of an ideal of monomials

If $I$ is a proper ideal of $C[0,1]$ , then should there exist $a \in [0,1]$ such that $f(a)=0 , \forall f \in I$?

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