Question

Why is $I = \left \{ \sum_{i=0}^n a_i x^i | a_0 \in 2 \mathbb{Z} \right \} \subseteq \mathbb{Z}[x]$ not a principal ideal?

score 52 · Answer 1 · 2020-07-07 22:53:18

52

Views

Why is $I = \left \{ \sum_{i=0}^n a_i x^i | a_0 \in 2 \mathbb{Z} \right \} \subseteq \mathbb{Z}[x]$ not a principal ideal?

Published on 07 Jul 2020 - 22:53

score 46 · Answer 2 · 2020-07-10 16:06:15

46

Views

Show that $I$ is an ideal of $\mathbb{K}[x]$

Published on 10 Jul 2020 - 16:06

score 76 · Answer 3 · 2020-07-11 10:10:44

76

Views

Prove an equality between ideals in $\mathbb{C}[x, y]$.

Published on 11 Jul 2020 - 10:10

score 61 · Answer 4 · 2026-03-26 00:52:51

61

Views

UFD is also an ideal of a ring

Published on 26 Mar 2026 - 0:52

score 317 · Answer 5 · 2020-07-13 13:48:49

317

Views

Why every field is a local ring, but the ring of integers $\mathbb{Z}$ not?

Published on 13 Jul 2020 - 13:48

score 140 · Answer 6 · 2026-03-26 06:01:39

140

Views

Equivalency of the maximum and minimum conditions of idempotents of a ring

Published on 26 Mar 2026 - 6:01

score 71 · Answer 7 · 2020-07-14 23:29:05

71

Views

Prove $[\mathfrak g,\mathfrak g]$ is an ideal.

Published on 14 Jul 2020 - 23:29

score 496 · Answer 8 · 2026-03-30 13:37:24

496

Views

$H$ normal iff $Lie(H)$ is an ideal.

Published on 30 Mar 2026 - 13:37

score 906 · Answer 9 · 2026-03-25 20:19:48

906

Views

Exhibit the ideals of $\mathbb{Z}[x]/(2,x^3+1)$

Published on 25 Mar 2026 - 20:19

score 434 · Answer 10 · 2026-02-23 10:02:51

434

Views

How can I understand a hypocycloid as an ideal in a polynomial ring?

Published on 23 Feb 2026 - 10:02

score 65 · Answer 11 · 2026-03-29 17:27:07

65

Views

How $\{am + pn : m, n \in \mathbb{Z}\}=\langle 1 \rangle$?

Published on 29 Mar 2026 - 17:27

score 396 · Answer 12 · 2026-03-25 12:27:24

396

Views

Example of a ring with a unique two sided maximal ideal which is not a local ring (that is it has more than one left or right maximal ideals).

Published on 25 Mar 2026 - 12:27

score 155 · Answer 13 · 2026-03-29 05:49:43

155

Views

How do we interpret a zero sequence in the context of ideal theory?

Published on 29 Mar 2026 - 5:49

score 157 · Answer 14 · 2020-07-20 04:09:08

157

Views

Ideals $(X^2+1)$ and $(X^2+1, 7)$ of polynomial ring $\mathbb{Z}[X]$

Published on 20 Jul 2020 - 4:09

score 59 · Answer 15 · 2020-07-20 09:55:17

59

Views

How does the ring structure $10\mathbb{Z}/5\mathbb{Z}$

Published on 20 Jul 2020 - 9:55

List Question

Why is $I = \left \{ \sum_{i=0}^n a_i x^i | a_0 \in 2 \mathbb{Z} \right \} \subseteq \mathbb{Z}[x]$ not a principal ideal?

Show that $I$ is an ideal of $\mathbb{K}[x]$

Prove an equality between ideals in $\mathbb{C}[x, y]$.

UFD is also an ideal of a ring

Why every field is a local ring, but the ring of integers $\mathbb{Z}$ not?

Equivalency of the maximum and minimum conditions of idempotents of a ring

Prove $[\mathfrak g,\mathfrak g]$ is an ideal.

$H$ normal iff $Lie(H)$ is an ideal.

Exhibit the ideals of $\mathbb{Z}[x]/(2,x^3+1)$

How can I understand a hypocycloid as an ideal in a polynomial ring?

How $\{am + pn : m, n \in \mathbb{Z}\}=\langle 1 \rangle$?

Example of a ring with a unique two sided maximal ideal which is not a local ring (that is it has more than one left or right maximal ideals).

How do we interpret a zero sequence in the context of ideal theory?

Ideals $(X^2+1)$ and $(X^2+1, 7)$ of polynomial ring $\mathbb{Z}[X]$

How does the ring structure $10\mathbb{Z}/5\mathbb{Z}$

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