Question

$N_1N_2N_3=\{x\in F^{\times}| x^2\in N\}$

score 104 · Answer 1 · 2019-10-20 09:54:43

104

Views

$N_1N_2N_3=\{x\in F^{\times}| x^2\in N\}$

Published on 20 Oct 2019 - 9:54

score 400 · Answer 2 · 2019-10-20 22:24:13

400

Views

Characteristic polynomial of left multiplication equals minimal polynomial of element

Published on 20 Oct 2019 - 22:24

score 37 · Answer 3 · 2019-10-21 09:47:07

37

Views

Let $k$ be a number field, and $\{\alpha_i\}_{i=1}^r$ a $\mathbb Q$-basis of $k$. Why is $k=\mathbb Q(\alpha_1,\dots,\alpha_r)$?

Published on 21 Oct 2019 - 9:47

score 99 · Answer 4 · 2019-10-22 09:55:26

99

Views

Show that $\Bbb Q(α)/\Bbb Q$ is not a normal field extension.

Published on 22 Oct 2019 - 9:55

score 23 · Answer 5 · 2026-04-03 08:32:59

23

Views

Degree of the field extensions corresponding to the points trisecting a line

Published on 03 Apr 2026 - 8:32

score 107 · Answer 6 · 2019-10-23 03:46:38

107

Views

$\mathbb{Q}(\sqrt{p+\sqrt{p}})$ is Galois over $\mathbb{Q} \iff p=n^2+1$ for a prime $p$.

Published on 23 Oct 2019 - 3:46

score 113 · Answer 7 · 2026-04-01 04:35:30

113

Views

Proving an extension is Galois

Published on 01 Apr 2026 - 4:35

score 70 · Answer 8 · 2026-03-28 06:11:21

70

Views

Understanding Lang’s comment about Galois extensions under isomorphisms

Published on 28 Mar 2026 - 6:11

score 79 · Answer 9 · 2026-04-01 02:05:48

79

Views

$W$ is $\sigma$-invariant i.e., $\sigma(W) \subset W$ implies that $W$ has a basis consisting of elements of $\mathbb F_{q}^n.$

Published on 01 Apr 2026 - 2:05

score 82 · Answer 10 · 2019-10-25 10:46:06

82

Views

Calculate $[K(\alpha^2):K]$

Published on 25 Oct 2019 - 10:46

score 115 · Answer 11 · 2026-04-03 08:21:15

115

Views

Are there any number fields that extend $\mathbb C$?

Published on 03 Apr 2026 - 8:21

score 82 · Answer 12 · 2019-10-27 10:55:50

82

Views

Is $\mathbb{Q}(2^{1/6})\cong\mathbb{Q}(\sqrt2)(2^{1/6})$ true?

Published on 27 Oct 2019 - 10:55

score 59 · Answer 13 · 2019-10-27 14:36:17

59

Views

If A/k and B/k are normal, show that (A \cap B)/k is normal.

Published on 27 Oct 2019 - 14:36

score 92 · Answer 14 · 2019-10-27 22:58:28

92

Views

Degree of the extension $\mathbb Q\subseteq \mathbb Q(\sqrt{5},\sqrt[3]{2})$

Published on 27 Oct 2019 - 22:58

score 204 · Answer 15 · 2026-02-23 03:30:23

204

Views

Why the definition of Galois group in rotman’s Advanced modern algebra not considering repeated roots

Published on 23 Feb 2026 - 3:30

List Question

$N_1N_2N_3=\{x\in F^{\times}| x^2\in N\}$

Characteristic polynomial of left multiplication equals minimal polynomial of element

Let $k$ be a number field, and $\{\alpha_i\}_{i=1}^r$ a $\mathbb Q$-basis of $k$. Why is $k=\mathbb Q(\alpha_1,\dots,\alpha_r)$?

Show that $\Bbb Q(α)/\Bbb Q$ is not a normal field extension.

Degree of the field extensions corresponding to the points trisecting a line

$\mathbb{Q}(\sqrt{p+\sqrt{p}})$ is Galois over $\mathbb{Q} \iff p=n^2+1$ for a prime $p$.

Proving an extension is Galois

Understanding Lang’s comment about Galois extensions under isomorphisms

$W$ is $\sigma$-invariant i.e., $\sigma(W) \subset W$ implies that $W$ has a basis consisting of elements of $\mathbb F_{q}^n.$

Calculate $[K(\alpha^2):K]$

Are there any number fields that extend $\mathbb C$?

Is $\mathbb{Q}(2^{1/6})\cong\mathbb{Q}(\sqrt2)(2^{1/6})$ true?

If A/k and B/k are normal, show that (A \cap B)/k is normal.

Degree of the extension $\mathbb Q\subseteq \mathbb Q(\sqrt{5},\sqrt[3]{2})$

Why the definition of Galois group in rotman’s Advanced modern algebra not considering repeated roots

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