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 179 · Answer 1 · 2026-04-16 10:01:55

179

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 16 Apr 2026 - 10:01

score 77 · Answer 2 · 2026-04-16 04:54:35

77

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 16 Apr 2026 - 4:54

score 283 · Answer 3 · 2026-05-10 14:55:48

283

Views

On the annihilator of a certain quotient module

Published on 10 May 2026 - 14:55

score 56 · Answer 4 · 2026-05-10 13:28:09

56

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 10 May 2026 - 13:28

score 165 · Answer 5 · 2026-04-12 07:04:20

165

Views

Restriction of an ideal sheaf to a hypersurface

Published on 12 Apr 2026 - 7:04

score 56 · Answer 6 · 2026-05-10 13:28:09

56

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 10 May 2026 - 13:28

score 157 · Answer 7 · 2026-04-13 04:26:52

157

Views

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

Published on 13 Apr 2026 - 4:26

score 219 · Answer 8 · 2026-04-16 11:29:57

219

Views

Maximal ideals in a polynomial ring

Published on 16 Apr 2026 - 11:29

score 153 · Answer 9 · 2026-04-15 05:52:27

153

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 15 Apr 2026 - 5:52

score 94 · Answer 10 · 2026-04-13 20:36:47

94

Views

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

Published on 13 Apr 2026 - 20:36

score 829 · Answer 11 · 2026-04-14 23:04:42

829

Views

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

Published on 14 Apr 2026 - 23:04

score 94 · Answer 12 · 2026-05-10 14:48:27

94

Views

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

Published on 10 May 2026 - 14:48

score 188 · Answer 13 · 2026-05-07 19:48:05

188

Views

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

Published on 07 May 2026 - 19:48

score 118 · Answer 14 · 2026-04-10 22:31:06

118

Views

Prime ring with identity and finite ideal

Published on 10 Apr 2026 - 22:31

score 2.3k · Answer 15 · 2026-04-15 17:49:08

2.3k

Views

Smallest ideal containing elements is the generated ideal

Published on 15 Apr 2026 - 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

Trending Questions

Popular # Hahtags

Popular Questions