Question

Prove that if $p(x)$ is irreducible, then $\langle p(x) \rangle$ is a maximal ideal of $F[x]$

score 1.9k · Answer 1 · 2019-05-13 15:48:20

1.9k

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Prove that if $p(x)$ is irreducible, then $\langle p(x) \rangle$ is a maximal ideal of $F[x]$

Published on 13 May 2019 - 15:48

score 38 · Answer 2 · 2019-05-13 16:19:59

38

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Is $\langle\bigcup_{i=1}^nA_i\rangle=A_1+\cdots+A_n$ always true for subsets $A_i$ in ring?

Published on 13 May 2019 - 16:19

score 117 · Answer 3 · 2026-03-25 12:27:05

117

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Proving $f(x)=x^4+4x^3+3x^2+7x-4$ is irreducible

Published on 25 Mar 2026 - 12:27

score 177 · Answer 4 · 2026-03-25 16:02:07

177

Views

Sufficient conditions for an element to be a unit in a euclidean domain

Published on 25 Mar 2026 - 16:02

score 9.8k · Answer 5 · 2026-03-28 10:40:37

9.8k

Views

Compute polynomial $p(x)$ if $x^5=1,\, x\neq 1$ [reducing mod $\textit{simpler}$ multiples]

Published on 28 Mar 2026 - 10:40

score 94 · Answer 6 · 2026-04-01 07:55:04

94

Views

Exact sequence of abelian groups

Published on 01 Apr 2026 - 7:55

score 196 · Answer 7 · 2019-05-14 01:15:16

196

Views

Establishing isomorphisms between polynomial quotient rings

Published on 14 May 2019 - 1:15

score 83 · Answer 8 · 2019-05-14 04:39:01

83

Views

Why can't we use different approach on the last problem of Exercise 2.11 of Atiyah-Macdonal?

Published on 14 May 2019 - 4:39

score 55 · Answer 9 · 2026-04-07 06:42:59

55

Views

$R=\mathbb{Q}[x]$ and $J=\langle x^2\rangle$, Is $R/J$ a principal ideal ring?

Published on 07 Apr 2026 - 6:42

score 2.3k · Answer 10 · 2026-03-28 01:06:44

2.3k

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Show $4x^2+6x+3$ is a unit in $\mathbb{Z}_8[x]$ (inverting unit + nilpotent)

Published on 28 Mar 2026 - 1:06

score 194 · Answer 11 · 2019-05-14 15:37:56

194

Views

$\mathbb{Z}[\alpha]$ is a euclidean ring.

Published on 14 May 2019 - 15:37

score 142 · Answer 12 · 2026-04-02 14:35:47

142

Views

On Hopfian modules over commutative Noetherian rings

Published on 02 Apr 2026 - 14:35

score 339 · Answer 13 · 2019-05-15 07:49:30

339

Views

Prove that $\mathbb{C}[x]/(x^2+2x)$ is isomorphic to $\mathbb{C} \oplus \mathbb{C} $

Published on 15 May 2019 - 7:49

score 217 · Answer 14 · 2026-03-31 20:25:23

217

Views

Map induced on fraction fields is finite

Published on 31 Mar 2026 - 20:25

score 210 · Answer 15 · 2026-04-02 14:35:33

210

Views

Endomorphism rings of indecomposable modules

Published on 02 Apr 2026 - 14:35

List Question

Prove that if $p(x)$ is irreducible, then $\langle p(x) \rangle$ is a maximal ideal of $F[x]$

Is $\langle\bigcup_{i=1}^nA_i\rangle=A_1+\cdots+A_n$ always true for subsets $A_i$ in ring?

Proving $f(x)=x^4+4x^3+3x^2+7x-4$ is irreducible

Sufficient conditions for an element to be a unit in a euclidean domain

Compute polynomial $p(x)$ if $x^5=1,\, x\neq 1$ [reducing mod $\textit{simpler}$ multiples]

Exact sequence of abelian groups

Establishing isomorphisms between polynomial quotient rings

Why can't we use different approach on the last problem of Exercise 2.11 of Atiyah-Macdonal?

$R=\mathbb{Q}[x]$ and $J=\langle x^2\rangle$, Is $R/J$ a principal ideal ring?

Show $4x^2+6x+3$ is a unit in $\mathbb{Z}_8[x]$ (inverting unit + nilpotent)

$\mathbb{Z}[\alpha]$ is a euclidean ring.

On Hopfian modules over commutative Noetherian rings

Prove that $\mathbb{C}[x]/(x^2+2x)$ is isomorphic to $\mathbb{C} \oplus \mathbb{C} $

Map induced on fraction fields is finite

Endomorphism rings of indecomposable modules

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