Question

Ideals $\neq0$ in $F[x]$ & Euclidean domains are generated by elements $\neq0$ of minimal degree (Euclidean size), so Euclidean $\Rightarrow$ PID

score 955 · Answer 1 · 2019-07-10 19:47:09

955

Views

Ideals $\neq0$ in $F[x]$ & Euclidean domains are generated by elements $\neq0$ of minimal degree (Euclidean size), so Euclidean $\Rightarrow$ PID

Published on 10 Jul 2019 - 19:47

score 146 · Answer 2 · 2026-03-29 17:06:53

146

Views

Which are the possible maximal ideals in $C[0,1]$ containing a prime which is not maximal?

Published on 29 Mar 2026 - 17:06

score 119 · Answer 3 · 2026-03-27 05:41:54

119

Views

Show that the ideal $I = 3\mathbb Z[x] + (x^3-x^2+2x-1)\mathbb Z[x]$ is not a principal ideal of $\mathbb Z[x]$

Published on 27 Mar 2026 - 5:41

score 84 · Answer 4 · 2026-03-27 07:18:53

84

Views

Show $\mathbb Z[x] / I \cong \overline{\mathbb Z}[x]/ \overline{I}$ where $\overline{\mathbb Z} = (\mathbb Z /3 \mathbb Z)$

Published on 27 Mar 2026 - 7:18

score 105 · Answer 5 · 2019-07-13 16:10:29

105

Views

Some question of ideal

Published on 13 Jul 2019 - 16:10

score 219 · Answer 6 · 2026-03-25 10:58:54

219

Views

How to show if $(f)=(c)(g)$ where $c \in R$ (UFD) and $g$ is primitive , then $(c)=(\mathrm{cont}_f)$ where $\mathrm{cont}_f$ is the content of $f$.

Published on 25 Mar 2026 - 10:58

score 167 · Answer 7 · 2026-03-25 09:28:36

167

Views

Semigroup structure of principal ideals (under products) in a Dedekind domain

Published on 25 Mar 2026 - 9:28

score 87 · Answer 8 · 2019-07-14 04:20:46

87

Views

Find the number of the ideals in this ring.

Published on 14 Jul 2019 - 4:20

score 234 · Answer 9 · 2019-07-14 19:33:30

234

Views

$\mathbb{C}$ as a quotient of $\mathbb{R}[x]$ by the principal ideal of $x^2 + 1$

Published on 14 Jul 2019 - 19:33

score 100 · Answer 10 · 2026-03-25 20:12:44

100

Views

$0 \subset (x_1 - a_1) \subset (x_1 - a_1, x_2-a_2) \subset ... \subset (x_1-a_1,..., x_n - a_n)$ is a (strictly) ascending chain of prime ideals

Published on 25 Mar 2026 - 20:12

score 294 · Answer 11 · 2026-03-30 17:46:19

294

Views

Is the sum of two solvable ideals is nilpotent?

Published on 30 Mar 2026 - 17:46

score 164 · Answer 12 · 2019-07-16 02:18:03

164

Views

If a polynomial $f$ is zero at $(a_1,...,a_k,x_{k+1},...,x_{n})$ then $f$ lies in the ideal $(x_1-a_1,...,x_n - a_n)?$

Published on 16 Jul 2019 - 2:18

score 208 · Answer 13 · 2026-03-27 18:26:17

208

Views

Normal subgroup and ideal inclusion

Published on 27 Mar 2026 - 18:26

score 54 · Answer 14 · 2019-07-18 09:56:32

54

Views

Show that $\ I=(x^n) $ for some $n$, an element of $\Bbb N\cup\{0\}$.

Published on 18 Jul 2019 - 9:56

score 126 · Answer 15 · 2019-07-20 17:20:13

126

Views

preimage of integral extension of ideal

Published on 20 Jul 2019 - 17:20

List Question

Ideals $\neq0$ in $F[x]$ & Euclidean domains are generated by elements $\neq0$ of minimal degree (Euclidean size), so Euclidean $\Rightarrow$ PID

Which are the possible maximal ideals in $C[0,1]$ containing a prime which is not maximal?

Show that the ideal $I = 3\mathbb Z[x] + (x^3-x^2+2x-1)\mathbb Z[x]$ is not a principal ideal of $\mathbb Z[x]$

Show $\mathbb Z[x] / I \cong \overline{\mathbb Z}[x]/ \overline{I}$ where $\overline{\mathbb Z} = (\mathbb Z /3 \mathbb Z)$

Some question of ideal

How to show if $(f)=(c)(g)$ where $c \in R$ (UFD) and $g$ is primitive , then $(c)=(\mathrm{cont}_f)$ where $\mathrm{cont}_f$ is the content of $f$.

Semigroup structure of principal ideals (under products) in a Dedekind domain

Find the number of the ideals in this ring.

$\mathbb{C}$ as a quotient of $\mathbb{R}[x]$ by the principal ideal of $x^2 + 1$

$0 \subset (x_1 - a_1) \subset (x_1 - a_1, x_2-a_2) \subset ... \subset (x_1-a_1,..., x_n - a_n)$ is a (strictly) ascending chain of prime ideals

Is the sum of two solvable ideals is nilpotent?

If a polynomial $f$ is zero at $(a_1,...,a_k,x_{k+1},...,x_{n})$ then $f$ lies in the ideal $(x_1-a_1,...,x_n - a_n)?$

Normal subgroup and ideal inclusion

Show that $\ I=(x^n) $ for some $n$, an element of $\Bbb N\cup\{0\}$.

preimage of integral extension of ideal

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