Question

Prove that $\alpha^2-3\alpha+1$ is not in the ideal $(5,\alpha+2)$ in $\mathbb{Z[\alpha]}$ where $\alpha=2^{1/3}$

score 176 · Answer 1 · 2018-03-18 02:59:27

176

Views

Prove that $\alpha^2-3\alpha+1$ is not in the ideal $(5,\alpha+2)$ in $\mathbb{Z[\alpha]}$ where $\alpha=2^{1/3}$

Published on 18 Mar 2018 - 2:59

score 74 · Answer 2 · 2018-03-18 04:32:48

74

Views

Let $A$ an $R$-ideal, $M$ a submodule generated by $n$ elements, $x \in R$ with $xM \subset AM$. Show that $(x^n+y)M = 0$ for some $y \in A$

Published on 18 Mar 2018 - 4:32

score 279 · Answer 3 · 2018-03-18 17:03:00

279

Views

On the annihilator of a certain quotient module

Published on 18 Mar 2018 - 17:03

score 53 · Answer 4 · 2026-03-25 06:22:07

53

Views

On finite generation of $IM$ where $M$ is an $R$-module and $I=Ann_R (M/N)$ , where $N$ is a finitely generated submodule of $M$

Published on 25 Mar 2026 - 6:22

score 162 · Answer 5 · 2018-03-18 22:07:28

162

Views

Restriction of an ideal sheaf to a hypersurface

Published on 18 Mar 2018 - 22:07

score 53 · Answer 6 · 2026-03-25 06:22:07

53

Views

On finite generation of a submodule $N$ of a finitely generated $R$-module $M$, such that $IM$ is finitely generated, where $I=Ann_R (M/N)$

Published on 25 Mar 2026 - 6:22

score 154 · Answer 7 · 2018-03-19 15:56:44

154

Views

Generated ideal of an Element with $x=x^{2}$

Published on 19 Mar 2018 - 15:56

score 216 · Answer 8 · 2018-03-19 17:26:40

216

Views

Maximal ideals in a polynomial ring

Published on 19 Mar 2018 - 17:26

score 151 · Answer 9 · 2018-03-19 19:23:26

151

Views

$A$ is a ring and $I$ is an ideal, an element $x \in A$ maps to an invertible element of $A/I$.

Published on 19 Mar 2018 - 19:23

score 91 · Answer 10 · 2018-03-21 08:36:10

91

Views

How many $n$ such that the ideal $\langle n, x \rangle$ in $\mathbb{Z}{[x]}$ is principal?

Published on 21 Mar 2018 - 8:36

score 826 · Answer 11 · 2018-03-22 17:08:12

826

Views

Under what circumstances is $I$ a free R-module?

Published on 22 Mar 2018 - 17:08

score 89 · Answer 12 · 2026-03-24 23:44:34

89

Views

Can the Artin-Rees lemma be derived from Krull Intersection theorem?

Published on 24 Mar 2026 - 23:44

score 180 · Answer 13 · 2026-03-19 22:26:57

180

Views

Associative algebra without nilpotent ideals is direct sum of minimal left ideals

Published on 19 Mar 2026 - 22:26

score 115 · Answer 14 · 2018-03-25 15:43:21

115

Views

Prime ring with identity and finite ideal

Published on 25 Mar 2018 - 15:43

score 2.3k · Answer 15 · 2018-03-25 17:49:42

2.3k

Views

Smallest ideal containing elements is the generated ideal

Published on 25 Mar 2018 - 17:49

List Question

Prove that $\alpha^2-3\alpha+1$ is not in the ideal $(5,\alpha+2)$ in $\mathbb{Z[\alpha]}$ where $\alpha=2^{1/3}$

Let $A$ an $R$-ideal, $M$ a submodule generated by $n$ elements, $x \in R$ with $xM \subset AM$. Show that $(x^n+y)M = 0$ for some $y \in A$

On the annihilator of a certain quotient module

On finite generation of $IM$ where $M$ is an $R$-module and $I=Ann_R (M/N)$ , where $N$ is a finitely generated submodule of $M$

Restriction of an ideal sheaf to a hypersurface

On finite generation of a submodule $N$ of a finitely generated $R$-module $M$, such that $IM$ is finitely generated, where $I=Ann_R (M/N)$

Generated ideal of an Element with $x=x^{2}$

Maximal ideals in a polynomial ring

$A$ is a ring and $I$ is an ideal, an element $x \in A$ maps to an invertible element of $A/I$.

How many $n$ such that the ideal $\langle n, x \rangle$ in $\mathbb{Z}{[x]}$ is principal?

Under what circumstances is $I$ a free R-module?

Can the Artin-Rees lemma be derived from Krull Intersection theorem?

Associative algebra without nilpotent ideals is direct sum of minimal left ideals

Prime ring with identity and finite ideal

Smallest ideal containing elements is the generated ideal

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