Question

$f$ a ring epimorphism and $\alpha$ an ideal then $f(\sqrt{\alpha}) = \sqrt{\alpha^e}$

score 56 · Answer 1 · 2018-01-31 00:05:05

56

Views

$f$ a ring epimorphism and $\alpha$ an ideal then $f(\sqrt{\alpha}) = \sqrt{\alpha^e}$

Published on 31 Jan 2018 - 0:05

score 805 · Answer 2 · 2026-03-25 04:43:39

805

Views

Let $R$ be a ring of prime characteristic. Say $a\in R$ and $a$ is nilpotent. Prove that $1+a$ is unipotent.

Published on 25 Mar 2026 - 4:43

score 671 · Answer 3 · 2018-01-31 06:37:34

671

Views

Rank of a submodule less or equal to the rank of the module?

Published on 31 Jan 2018 - 6:37

score 289 · Answer 4 · 2026-03-25 07:16:37

289

Views

Nil ideal of the ring of integers modulo $n$

Published on 25 Mar 2026 - 7:16

score 347 · Answer 5 · 2026-03-20 09:35:06

347

Views

A characterization for minimal left ideals of semisimple rings

Published on 20 Mar 2026 - 9:35

score 114 · Answer 6 · 2018-01-31 12:21:01

114

Views

$\Omega^1_{B/A}=0$ implies $B$ normal

Published on 31 Jan 2018 - 12:21

score 184 · Answer 7 · 2026-03-22 05:13:36

184

Views

Quotient of normal ring by principal ideal

Published on 22 Mar 2026 - 5:13

score 506 · Answer 8 · 2026-03-20 08:58:19

506

Views

On the radical of an ideal in the polynomial ring in 4 variables over complex field

Published on 20 Mar 2026 - 8:58

score 64 · Answer 9 · 2026-03-20 08:48:32

64

Views

$A \subseteq B \subseteq C$, with $A$ and $C$ simple rings, but $B$ is not a simple ring

Published on 20 Mar 2026 - 8:48

score 107 · Answer 10 · 2018-01-31 22:56:40

107

Views

Show that $(R^{\times}, \cdot)$ form a group

Published on 31 Jan 2018 - 22:56

score 103 · Answer 11 · 2026-03-20 06:50:51

103

Views

Simplicity of Noetherian $B$, $A \subseteq B\subseteq C$, where $A$ and $C$ are simple Noetherian domains

Published on 20 Mar 2026 - 6:50

score 576 · Answer 12 · 2018-02-01 00:02:18

576

Views

Show that $\mathbb{Z}\left[\frac{1+\sqrt{-3}}{2}\right]$ is a Euclidean Domain.

Published on 01 Feb 2018 - 0:02

score 764 · Answer 13 · 2026-03-20 09:33:13

764

Views

Let $φ:\mathbb{C[x,y,z]}\to \mathbb{C[t]}$ by $φ(f(x,y,z))=f(t,t^2,t^3)$. Find generators for ker($φ$)

Published on 20 Mar 2026 - 9:33

score 88 · Answer 14 · 2026-03-23 09:25:49

88

Views

Is $\mathbb R[x]/(x^2-2)=\mathbb R$?

Published on 23 Mar 2026 - 9:25

score 357 · Answer 15 · 2026-03-24 22:13:59

357

Views

How do I know if an ideal $I$ in $\mathbb Z[x]$ is principal? maximal?

Published on 24 Mar 2026 - 22:13

List Question

$f$ a ring epimorphism and $\alpha$ an ideal then $f(\sqrt{\alpha}) = \sqrt{\alpha^e}$

Let $R$ be a ring of prime characteristic. Say $a\in R$ and $a$ is nilpotent. Prove that $1+a$ is unipotent.

Rank of a submodule less or equal to the rank of the module?

Nil ideal of the ring of integers modulo $n$

A characterization for minimal left ideals of semisimple rings

$\Omega^1_{B/A}=0$ implies $B$ normal

Quotient of normal ring by principal ideal

On the radical of an ideal in the polynomial ring in 4 variables over complex field

$A \subseteq B \subseteq C$, with $A$ and $C$ simple rings, but $B$ is not a simple ring

Show that $(R^{\times}, \cdot)$ form a group

Simplicity of Noetherian $B$, $A \subseteq B\subseteq C$, where $A$ and $C$ are simple Noetherian domains

Show that $\mathbb{Z}\left[\frac{1+\sqrt{-3}}{2}\right]$ is a Euclidean Domain.

Let $φ:\mathbb{C[x,y,z]}\to \mathbb{C[t]}$ by $φ(f(x,y,z))=f(t,t^2,t^3)$. Find generators for ker($φ$)

Is $\mathbb R[x]/(x^2-2)=\mathbb R$?

How do I know if an ideal $I$ in $\mathbb Z[x]$ is principal? maximal?

Trending Questions

Popular # Hahtags

Popular Questions