Question

diagonal action induces permutation

score 108 · Answer 1 · 2014-04-26 13:00:51

108

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diagonal action induces permutation

Published on 26 Apr 2014 - 13:00

score 748 · Answer 2 · 2014-04-26 19:07:01

748

Views

Splitting field for primitive element of Galois extension and description of Galois group

Published on 26 Apr 2014 - 19:07

score 127 · Answer 3 · 2014-04-26 21:00:01

127

Views

How do I proof that Aut(E/F) is a group? (E is an extension field of F)

Published on 26 Apr 2014 - 21:00

score 2.6k · Answer 4 · 2026-03-26 06:32:42

2.6k

Views

Let $K = \mathbb{Q}(\alpha)$ where $\alpha$ is a root of the polynomial $x^3 + 2x + 1$, and let $g(x) = x^3 + x + 1$. Does $g(x)$ have a root in $K$?

Published on 26 Mar 2026 - 6:32

score 64 · Answer 5 · 2014-04-27 01:20:08

64

Views

Help to prove fact about Galois Theory?

Published on 27 Apr 2014 - 1:20

score 928 · Answer 6 · 2026-03-25 12:15:30

928

Views

Prove that $F(\sqrt{\alpha}) = F(\sqrt{\beta})$

Published on 25 Mar 2026 - 12:15

score 132 · Answer 7 · 2026-03-26 21:26:21

132

Views

How can I prove that $[\mathbb{Q}(\omega + \omega^{-1}) :\mathbb{Q}]=\frac{\varphi (n)}{2}$?

Published on 26 Mar 2026 - 21:26

score 59 · Answer 8 · 2014-04-28 01:16:35

59

Views

isomorphic to Galois group of the polynomial $(x-1)^2(x-3)^3(x-5)$

Published on 28 Apr 2014 - 1:16

score 39 · Answer 9 · 2014-04-28 01:51:39

39

Views

Help to prove fact about quintic and galois theory?

Published on 28 Apr 2014 - 1:51

score 268 · Answer 10 · 2026-03-26 08:03:59

268

Views

Understanding a Solution (Splitting Fields)

Published on 26 Mar 2026 - 8:03

score 260 · Answer 11 · 2014-04-28 20:00:01

260

Views

Is there a typo in this proof about Galois theory in Artin's Algebra?

Published on 28 Apr 2014 - 20:00

score 853 · Answer 12 · 2014-04-29 03:38:31

853

Views

Complex Conjugation as an $F$-Automorphism of $K$?

Published on 29 Apr 2014 - 3:38

score 338 · Answer 13 · 2014-04-29 06:53:55

338

Views

Given $f(x) = x^3 + x + 1$, is $\sqrt{-31}$ in $\mathbb{Q}[x]/(f)$? In the splitting field $K$ of $f$?

Published on 29 Apr 2014 - 6:53

score 258 · Answer 14 · 2026-03-25 09:23:34

258

Views

Clarification of Abel-Ruffini theorem statement

Published on 25 Mar 2026 - 9:23

score 1.9k · Answer 15 · 2026-03-30 05:28:57

1.9k

Views

Irreducible Polynomials over a Finite Field

Published on 30 Mar 2026 - 5:28

List Question

diagonal action induces permutation

Splitting field for primitive element of Galois extension and description of Galois group

How do I proof that Aut(E/F) is a group? (E is an extension field of F)

Let $K = \mathbb{Q}(\alpha)$ where $\alpha$ is a root of the polynomial $x^3 + 2x + 1$, and let $g(x) = x^3 + x + 1$. Does $g(x)$ have a root in $K$?

Help to prove fact about Galois Theory?

Prove that $F(\sqrt{\alpha}) = F(\sqrt{\beta})$

How can I prove that $[\mathbb{Q}(\omega + \omega^{-1}) :\mathbb{Q}]=\frac{\varphi (n)}{2}$?

isomorphic to Galois group of the polynomial $(x-1)^2(x-3)^3(x-5)$

Help to prove fact about quintic and galois theory?

Understanding a Solution (Splitting Fields)

Is there a typo in this proof about Galois theory in Artin's Algebra?

Complex Conjugation as an $F$-Automorphism of $K$?

Given $f(x) = x^3 + x + 1$, is $\sqrt{-31}$ in $\mathbb{Q}[x]/(f)$? In the splitting field $K$ of $f$?

Clarification of Abel-Ruffini theorem statement

Irreducible Polynomials over a Finite Field

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