Question

An Ideal I of $ \mathbb Z[\sqrt 3]$ generated by an integer prime, such that $\mathbb Z[ \sqrt 3]/I$ is not an integral domain.

score 715 · Answer 1 · 2026-03-25 09:29:23

715

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An Ideal I of $ \mathbb Z[\sqrt 3]$ generated by an integer prime, such that $\mathbb Z[ \sqrt 3]/I$ is not an integral domain.

Published on 25 Mar 2026 - 9:29

score 161 · Answer 2 · 2019-03-27 01:35:19

161

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Basic Questions About Ideals

Published on 27 Mar 2019 - 1:35

score 41 · Answer 3 · 2019-03-27 18:12:58

41

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Prove that $p(X,Y)\mapsto p(i,-i)$'s kernel is the ideal $(X+Y,X^2+1)$

Published on 27 Mar 2019 - 18:12

score 59 · Answer 4 · 2019-03-28 11:57:42

59

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Algebraic Geometry: Let $\varphi: k[X,Y] \rightarrow k(t)$ defined by $\varphi (f(X,Y)) = f(\frac{1-t^2}{t^2+1},\frac{2t}{t^2+1})$ .

Published on 28 Mar 2019 - 11:57

score 284 · Answer 5 · 2026-03-25 13:54:50

284

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Duality between Ideal and Filters on a poset

Published on 25 Mar 2026 - 13:54

score 893 · Answer 6 · 2019-03-29 16:22:33

893

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Generators of Principal Ideal

Published on 29 Mar 2019 - 16:22

score 289 · Answer 7 · 2019-03-30 15:52:32

289

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Image of arbitrary ideal under quotient map

Published on 30 Mar 2019 - 15:52

score 50 · Answer 8 · 2019-03-31 17:50:33

50

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Simple exercise about ideals of integers

Published on 31 Mar 2019 - 17:50

score 93 · Answer 9 · 2026-03-27 21:22:22

93

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What is the ideal class group?

Published on 27 Mar 2026 - 21:22

score 32 · Answer 10 · 2026-03-25 13:55:29

32

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A nice way to phrase this theorem about ideals in Noetherian rings?

Published on 25 Mar 2026 - 13:55

score 66 · Answer 11 · 2019-04-02 02:27:17

66

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Find a prime $P$ such that a given ideal is $P$-primary

Published on 02 Apr 2019 - 2:27

score 97 · Answer 12 · 2026-03-25 21:56:04

97

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Is there a way to extract a primary decomposition of $(0)\subset R/I$ given a decomposition of $I\subset R$?

Published on 25 Mar 2026 - 21:56

score 93 · Answer 13 · 2026-03-25 13:54:43

93

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Two Sided Ideal in Left-Localization of a Left-Noetherian Ring

Published on 25 Mar 2026 - 13:54

score 71 · Answer 14 · 2026-03-25 13:58:00

71

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Grillet's "Abstract Algebra", p. 148, ex. 3: Noetherian subring of a ring

Published on 25 Mar 2026 - 13:58

score 234 · Answer 15 · 2026-03-25 13:56:47

234

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Is Axiom of Dependence Choice necessary for two definitions of Noetherian to be equivalent?

Published on 25 Mar 2026 - 13:56

List Question

An Ideal I of $ \mathbb Z[\sqrt 3]$ generated by an integer prime, such that $\mathbb Z[ \sqrt 3]/I$ is not an integral domain.

Basic Questions About Ideals

Prove that $p(X,Y)\mapsto p(i,-i)$'s kernel is the ideal $(X+Y,X^2+1)$

Algebraic Geometry: Let $\varphi: k[X,Y] \rightarrow k(t)$ defined by $\varphi (f(X,Y)) = f(\frac{1-t^2}{t^2+1},\frac{2t}{t^2+1})$ .

Duality between Ideal and Filters on a poset

Generators of Principal Ideal

Image of arbitrary ideal under quotient map

Simple exercise about ideals of integers

What is the ideal class group?

A nice way to phrase this theorem about ideals in Noetherian rings?

Find a prime $P$ such that a given ideal is $P$-primary

Is there a way to extract a primary decomposition of $(0)\subset R/I$ given a decomposition of $I\subset R$?

Two Sided Ideal in Left-Localization of a Left-Noetherian Ring

Grillet's "Abstract Algebra", p. 148, ex. 3: Noetherian subring of a ring

Is Axiom of Dependence Choice necessary for two definitions of Noetherian to be equivalent?

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