Question

The quotient of an integral extension is also an integral extension

score 164 · Answer 1 · 2026-04-14 13:32:17

164

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The quotient of an integral extension is also an integral extension

Published on 14 Apr 2026 - 13:32

score 156 · Answer 2 · 2026-04-17 22:35:22

156

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What is the dimension of the vector space $\mathbb Q [x]$/$((x+1)^2)$

Published on 17 Apr 2026 - 22:35

score 121 · Answer 3 · 2026-04-09 10:15:52

121

Views

Galois group of $x^5-x-1$ over $\Bbb Q$ using integral extension ring theory

Published on 09 Apr 2026 - 10:15

score 43 · Answer 4 · 2026-04-16 01:16:40

43

Views

The homomorphic image of the intermediate field

Published on 16 Apr 2026 - 1:16

score 147 · Answer 5 · 2026-04-16 04:38:14

147

Views

Integers $a$ such that $\mathbb{Q}(\alpha)$ has no intermediate subfields where $\alpha$ is a root of $T^4 - aT - 1$

Published on 16 Apr 2026 - 4:38

score 161 · Answer 6 · 2026-04-12 05:29:08

161

Views

Are the two definitions of a perfect ring in Wikipedia related?

Published on 12 Apr 2026 - 5:29

score 307 · Answer 7 · 2026-04-09 13:38:18

307

Views

Can the ''Galois group" for an inseparable irreducible polynomial of degree 4 be $S_{3}$?

Published on 09 Apr 2026 - 13:38

score 30 · Answer 8 · 2026-04-09 18:16:33

30

Views

Constructive proof of fiinite extension implies algebraic

Published on 09 Apr 2026 - 18:16

score 69 · Answer 9 · 2026-03-26 14:28:08

69

Views

Proof verification on Field Extension

Published on 26 Mar 2026 - 14:28

score 77 · Answer 10 · 2026-04-12 01:58:32

77

Views

Finding all Subfields

Published on 12 Apr 2026 - 1:58

score 384 · Answer 11 · 2026-03-28 18:16:02

384

Views

Why should the real numbers interact with number fields and Galois theory?

Published on 28 Mar 2026 - 18:16

score 176 · Answer 12 · 2026-04-17 10:31:21

176

Views

Find the least prime $p$ such that $x^{22} + x^{21} + \cdots + x + 1$ irreducible over $F_p$.

Published on 17 Apr 2026 - 10:31

score 308 · Answer 13 · 2026-03-28 20:22:24

308

Views

Proposition 14.21 in the book "Abstract Algebra" by Dummit and Foote

Published on 28 Mar 2026 - 20:22

score 59 · Answer 14 · 2026-03-26 16:06:03

59

Views

Prove if $R$ is not a field then the value set $δ(R)$ is infinite, $δ$ a Euclidean degree function.

Published on 26 Mar 2026 - 16:06

score 82 · Answer 15 · 2026-04-16 19:04:31

82

Views

showing $x^4+x^2+x+1$ is reducible in $GF(81)=GF(3^4)$

Published on 16 Apr 2026 - 19:04

List Question

The quotient of an integral extension is also an integral extension

What is the dimension of the vector space $\mathbb Q [x]$/$((x+1)^2)$

Galois group of $x^5-x-1$ over $\Bbb Q$ using integral extension ring theory

The homomorphic image of the intermediate field

Integers $a$ such that $\mathbb{Q}(\alpha)$ has no intermediate subfields where $\alpha$ is a root of $T^4 - aT - 1$

Are the two definitions of a perfect ring in Wikipedia related?

Can the ''Galois group" for an inseparable irreducible polynomial of degree 4 be $S_{3}$?

Constructive proof of fiinite extension implies algebraic

Proof verification on Field Extension

Finding all Subfields

Why should the real numbers interact with number fields and Galois theory?

Find the least prime $p$ such that $x^{22} + x^{21} + \cdots + x + 1$ irreducible over $F_p$.

Proposition 14.21 in the book "Abstract Algebra" by Dummit and Foote

Prove if $R$ is not a field then the value set $δ(R)$ is infinite, $δ$ a Euclidean degree function.

showing $x^4+x^2+x+1$ is reducible in $GF(81)=GF(3^4)$

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