Question

Is it true every ideal of $\mathbb{Z}[x]$ is finitely generated?

score 543 · Answer 1 · 2026-03-25 10:56:03

543

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Is it true every ideal of $\mathbb{Z}[x]$ is finitely generated?

Published on 25 Mar 2026 - 10:56

score 130 · Answer 2 · 2019-02-21 14:43:27

130

Views

How to prove this isomorphism of a quotient ring

Published on 21 Feb 2019 - 14:43

score 903 · Answer 3 · 2019-02-23 11:12:36

903

Views

Product of the two subrings

Published on 23 Feb 2019 - 11:12

score 73 · Answer 4 · 2019-02-23 18:21:33

73

Views

Is this ideal principal?

Published on 23 Feb 2019 - 18:21

score 136 · Answer 5 · 2019-02-24 12:01:57

136

Views

Finding all ideals $T$ in number ring $\mathbb Z[\sqrt{-3}]$ s.t. $\langle 4 \rangle \subset T$.

Published on 24 Feb 2019 - 12:01

score 107 · Answer 6 · 2019-02-25 18:39:09

107

Views

Why is $6\mathbb{Z} + 9\mathbb{Z}$ a principal ideal of $\mathbb{Z}$?

Published on 25 Feb 2019 - 18:39

score 575 · Answer 7 · 2026-03-25 14:20:14

575

Views

Units in a discrete valuation ring.

Published on 25 Mar 2026 - 14:20

score 35 · Answer 8 · 2026-03-28 07:36:28

35

Views

Find an element that generates the Ideal

Published on 28 Mar 2026 - 7:36

score 3.4k · Answer 9 · 2019-02-26 18:50:11

3.4k

Views

How to find an ideal of a ring

Published on 26 Feb 2019 - 18:50

score 88 · Answer 10 · 2026-03-25 06:58:55

88

Views

If $R$ is an n-fir, why free $R$-modules of rank at most $n$ have unique rank?

Published on 25 Mar 2026 - 6:58

score 223 · Answer 11 · 2026-03-26 02:55:57

223

Views

Localization of the polynomial ring at a prime ideal modulo maximal ideal is isomorphic to polynomial ring modulo prime ideal.

Published on 26 Mar 2026 - 2:55

score 137 · Answer 12 · 2026-03-29 10:15:18

137

Views

There exists a prime ideal not containing non-nilpotent element

Published on 29 Mar 2026 - 10:15

score 124 · Answer 13 · 2019-03-01 07:18:30

124

Views

Does a ring homomorphism $\phi: R \rightarrow S$ give rise to any map $\psi: R/I \rightarrow S/J?$

Published on 01 Mar 2019 - 7:18

score 269 · Answer 14 · 2019-03-04 00:46:18

269

Views

$M_{i+1}/M_i\simeq R/P_i$ for some prime ideal $P_i$

Published on 04 Mar 2019 - 0:46

score 71 · Answer 15 · 2026-03-25 19:05:26

71

Views

Is this an example of comaximal ideals $I,J$ such that $IJ\not=I\cap J$?

Published on 25 Mar 2026 - 19:05

List Question

Is it true every ideal of $\mathbb{Z}[x]$ is finitely generated?

How to prove this isomorphism of a quotient ring

Product of the two subrings

Is this ideal principal?

Finding all ideals $T$ in number ring $\mathbb Z[\sqrt{-3}]$ s.t. $\langle 4 \rangle \subset T$.

Why is $6\mathbb{Z} + 9\mathbb{Z}$ a principal ideal of $\mathbb{Z}$?

Units in a discrete valuation ring.

Find an element that generates the Ideal

How to find an ideal of a ring

If $R$ is an n-fir, why free $R$-modules of rank at most $n$ have unique rank?

Localization of the polynomial ring at a prime ideal modulo maximal ideal is isomorphic to polynomial ring modulo prime ideal.

There exists a prime ideal not containing non-nilpotent element

Does a ring homomorphism $\phi: R \rightarrow S$ give rise to any map $\psi: R/I \rightarrow S/J?$

$M_{i+1}/M_i\simeq R/P_i$ for some prime ideal $P_i$

Is this an example of comaximal ideals $I,J$ such that $IJ\not=I\cap J$?

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