Question

$K$ is a normal extension of$ F$ implies $ K $contains all the roots of minimal polynomial of $a$

score 81 · Answer 1 · 2018-06-03 07:28:59

81

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$K$ is a normal extension of$ F$ implies $ K $contains all the roots of minimal polynomial of $a$

Published on 03 Jun 2018 - 7:28

score 66 · Answer 2 · 2026-03-29 19:25:16

66

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Distinction between $\mathbb{K}(\alpha)$ and $\mathbb{K}[\alpha]$

Published on 29 Mar 2026 - 19:25

score 575 · Answer 3 · 2026-03-28 09:53:36

575

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Show that $\cdots\circ$ Fr$^{3!}\circ$Fr$^{2!}\circ$ Fr$^{1!} \in\operatorname{Gal}(\overline{\mathbb F_p}/\mathbb F_p)\setminus\langle$ Fr $\rangle$

Published on 28 Mar 2026 - 9:53

score 43 · Answer 4 · 2026-03-27 10:09:56

43

Views

Normal closure $L/k$ contains the Galois image of $k$

Published on 27 Mar 2026 - 10:09

score 434 · Answer 5 · 2026-03-26 02:46:48

434

Views

Is a proper ideal of a polynomial ring (on a field) still proper in the polynomial ring on a field extension?

Published on 26 Mar 2026 - 2:46

score 44 · Answer 6 · 2018-06-04 23:29:13

44

Views

When $f' \in k[f,g]$?

Published on 04 Jun 2018 - 23:29

score 139 · Answer 7 · 2018-06-05 00:06:07

139

Views

An intuitive way to interpret $\mathbb{Q}(\sqrt{a} + \sqrt{b})$

Published on 05 Jun 2018 - 0:06

score 204 · Answer 8 · 2018-06-05 01:05:23

204

Views

For which $f,g \in k[t]$, $k[f,g]$ is integrally closed?

Published on 05 Jun 2018 - 1:05

score 35 · Answer 9 · 2018-06-05 12:21:19

35

Views

$Q(m^{1/4})$ for $m$ non-square is degree 4 extension over $Q$?

Published on 05 Jun 2018 - 12:21

score 274 · Answer 10 · 2018-06-05 16:36:52

274

Views

Show that element is in field extension

Published on 05 Jun 2018 - 16:36

score 222 · Answer 11 · 2026-03-28 08:38:25

222

Views

Algebraic Torus: Etymology

Published on 28 Mar 2026 - 8:38

score 90 · Answer 12 · 2018-06-05 18:17:02

90

Views

$E/F$ a degree two field extension, can both E,F be isomorphic to Q(x) the field of rational functions?

Published on 05 Jun 2018 - 18:17

score 737 · Answer 13 · 2026-03-27 08:01:09

737

Views

Galois group of $x^3+2x+2$

Published on 27 Mar 2026 - 8:01

score 195 · Answer 14 · 2026-03-27 10:11:02

195

Views

Find Galois group of $\mathbb{Q} ( \sqrt{p})/\mathbb{Q}$

Published on 27 Mar 2026 - 10:11

score 101 · Answer 15 · 2026-03-25 13:13:36

101

Views

Find intermediate fields between $\mathbb{Q}$ and $\mathbb{Q}(2^{\frac{1}{4}}, i). $ Which of the extensions are normal over $\mathbb{Q}$?

Published on 25 Mar 2026 - 13:13

List Question

$K$ is a normal extension of$ F$ implies $ K $contains all the roots of minimal polynomial of $a$

Distinction between $\mathbb{K}(\alpha)$ and $\mathbb{K}[\alpha]$

Show that $\cdots\circ$ Fr$^{3!}\circ$Fr$^{2!}\circ$ Fr$^{1!} \in\operatorname{Gal}(\overline{\mathbb F_p}/\mathbb F_p)\setminus\langle$ Fr $\rangle$

Normal closure $L/k$ contains the Galois image of $k$

Is a proper ideal of a polynomial ring (on a field) still proper in the polynomial ring on a field extension?

When $f' \in k[f,g]$?

An intuitive way to interpret $\mathbb{Q}(\sqrt{a} + \sqrt{b})$

For which $f,g \in k[t]$, $k[f,g]$ is integrally closed?

$Q(m^{1/4})$ for $m$ non-square is degree 4 extension over $Q$?

Show that element is in field extension

Algebraic Torus: Etymology

$E/F$ a degree two field extension, can both E,F be isomorphic to Q(x) the field of rational functions?

Galois group of $x^3+2x+2$

Find Galois group of $\mathbb{Q} ( \sqrt{p})/\mathbb{Q}$

Find intermediate fields between $\mathbb{Q}$ and $\mathbb{Q}(2^{\frac{1}{4}}, i). $ Which of the extensions are normal over $\mathbb{Q}$?

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