Question

A field extension is separable iff it is contained in a Galois Extension

score 84 · Answer 1 · 2026-02-24 00:50:56

84

Views

A field extension is separable iff it is contained in a Galois Extension

Published on 24 Feb 2026 - 0:50

score 59 · Answer 2 · 2026-02-24 00:51:13

59

Views

Finding the roots of $x^5-2$. My question is about finding the $5^{th}$ roots of 2.While the associated question is about finding roots of unity

Published on 24 Feb 2026 - 0:51

score 119 · Answer 3 · 2022-10-09 18:59:30

119

Views

If $\alpha \in E$ is not fixed by any automorphism and $E$ is Galois, $E = F(\alpha)$.

Published on 09 Oct 2022 - 18:59

score 87 · Answer 4 · 2022-10-19 12:44:04

87

Views

Galois Theory: $ a = i\sqrt{2}+\sqrt{3}$.

Published on 19 Oct 2022 - 12:44

score 176 · Answer 5 · 2022-10-29 10:37:20

176

Views

Question about mapping of elements from $GF(2^8)$ to $GF((2^4)^2)?$

Published on 29 Oct 2022 - 10:37

score 91 · Answer 6 · 2026-03-28 13:41:48

91

Views

Doubt in Lang's proof of solvable extensions forming a distinguished class of extensions

Published on 28 Mar 2026 - 13:41

score 57 · Answer 7 · 2026-03-31 09:45:17

57

Views

Why isn't the crossed product algebra $(K(\sqrt{a}), Gal(K(\sqrt{a})/K, k)$ independent of a?

Published on 31 Mar 2026 - 9:45

score 54 · Answer 8 · 2026-03-28 13:36:25

54

Views

Effective degree bound for solvability by radicals

Published on 28 Mar 2026 - 13:36

score 73 · Answer 9 · 2022-12-07 04:19:51

73

Views

Help understanding why an automorphism is uniquely determined

Published on 07 Dec 2022 - 4:19

score 64 · Answer 10 · 2022-12-15 00:30:45

64

Views

Proving there are no intermediate normal extensions

Published on 15 Dec 2022 - 0:30

score 177 · Answer 11 · 2022-12-26 22:27:32

177

Views

Galois group of $x^n+x+1$

Published on 26 Dec 2022 - 22:27

score 137 · Answer 12 · 2026-02-24 01:36:23

137

Views

I am proposing two conjectures regarding the BCH codes ! Can anybody prove or disprove my conjectures?

Published on 24 Feb 2026 - 1:36

score 43 · Answer 13 · 2026-02-23 08:27:44

43

Views

Show there is a tower of cyclic field extensions of prime degree from $\mathbb{Q}(\sqrt[12]{5})$ to $\mathbb{Q}$

Published on 23 Feb 2026 - 8:27

score 180 · Answer 14 · 2023-01-02 21:05:45

180

Views

Galois group of the quintic $x^5 -11x + 1$.

Published on 02 Jan 2023 - 21:05

score 17 · Answer 15 · 2026-03-11 12:49:39

17

Views

Problem about cyclic extension of degree 4.

Published on 11 Mar 2026 - 12:49

List Question

A field extension is separable iff it is contained in a Galois Extension

Finding the roots of $x^5-2$. My question is about finding the $5^{th}$ roots of 2.While the associated question is about finding roots of unity

If $\alpha \in E$ is not fixed by any automorphism and $E$ is Galois, $E = F(\alpha)$.

Galois Theory: $ a = i\sqrt{2}+\sqrt{3}$.

Question about mapping of elements from $GF(2^8)$ to $GF((2^4)^2)?$

Doubt in Lang's proof of solvable extensions forming a distinguished class of extensions

Why isn't the crossed product algebra $(K(\sqrt{a}), Gal(K(\sqrt{a})/K, k)$ independent of a?

Effective degree bound for solvability by radicals

Help understanding why an automorphism is uniquely determined

Proving there are no intermediate normal extensions

Galois group of $x^n+x+1$

I am proposing two conjectures regarding the BCH codes ! Can anybody prove or disprove my conjectures?

Show there is a tower of cyclic field extensions of prime degree from $\mathbb{Q}(\sqrt[12]{5})$ to $\mathbb{Q}$

Galois group of the quintic $x^5 -11x + 1$.

Problem about cyclic extension of degree 4.

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