Question

Upper and lower bound on the degree of a field extension generated by two elements

score 246 · Answer 1 · 2018-05-02 06:26:42

246

Views

Upper and lower bound on the degree of a field extension generated by two elements

Published on 02 May 2018 - 6:26

score 178 · Answer 2 · 2018-05-03 03:19:25

178

Views

Fixed field and automorphisms. Galois Theory.

Published on 03 May 2018 - 3:19

score 118 · Answer 3 · 2018-05-03 08:14:17

118

Views

Searching for intermediate fields with the Galois correspondence

Published on 03 May 2018 - 8:14

score 54 · Answer 4 · 2018-05-03 14:29:13

54

Views

$p$ a prime and $p\equiv3\mod 4$, if $a^4=1_F$ where $F$ a field with characteristic $p$, then $x=a+a^{-1}\in F$

Published on 03 May 2018 - 14:29

score 78 · Answer 5 · 2026-03-25 11:25:58

78

Views

Algebraic closure of a real-closed field

Published on 25 Mar 2026 - 11:25

score 31 · Answer 6 · 2018-05-03 17:19:50

31

Views

Every normal extension has a subfield which is a galois extension?

Published on 03 May 2018 - 17:19

score 1.1k · Answer 7 · 2018-05-03 22:42:01

1.1k

Views

Show that the algebraic closure of $F$ in $K$ is an algebraic closure of $F$.

Published on 03 May 2018 - 22:42

score 2.5k · Answer 8 · 2018-05-04 05:52:18

2.5k

Views

Let $f(x)$ be an irreducible polynomial over $F$ of degree $n$, and let $K$ be a field extension of $F$ with $[K:F]=m$

Published on 04 May 2018 - 5:52

score 2.1k · Answer 9 · 2018-05-04 06:39:52

2.1k

Views

Determine the splitting field of $x^4 - 7$ over

Published on 04 May 2018 - 6:39

score 41 · Answer 10 · 2018-05-05 12:35:25

41

Views

Extensions field in Galois Theory. Check Proof.

Published on 05 May 2018 - 12:35

score 528 · Answer 11 · 2018-05-05 15:19:05

528

Views

Let $\sigma \in\operatorname{Aut}(K)$ have infinite order and $F = \mathcal{F}(\sigma)$. Show that if $K/F$ is algebraic, then $K$ is normal over $F$.

Published on 05 May 2018 - 15:19

score 49 · Answer 12 · 2018-05-06 09:28:28

49

Views

degree/dimension of field extension if $K=\Bbb Q(\alpha)$ and $F=\Bbb Q$

Published on 06 May 2018 - 9:28

score 314 · Answer 13 · 2026-03-25 08:07:35

314

Views

Isomorphism between two extensions $\Bbb F_2(\alpha)$ and $\Bbb F_2(\beta)$

Published on 25 Mar 2026 - 8:07

score 304 · Answer 14 · 2018-05-06 14:44:54

304

Views

Galois extension over a field of characteristic $0$ of order $2^n$

Published on 06 May 2018 - 14:44

score 72 · Answer 15 · 2018-05-06 16:16:26

72

Views

Arguing that an extension is not normal

Published on 06 May 2018 - 16:16

List Question

Upper and lower bound on the degree of a field extension generated by two elements

Fixed field and automorphisms. Galois Theory.

Searching for intermediate fields with the Galois correspondence

$p$ a prime and $p\equiv3\mod 4$, if $a^4=1_F$ where $F$ a field with characteristic $p$, then $x=a+a^{-1}\in F$

Algebraic closure of a real-closed field

Every normal extension has a subfield which is a galois extension?

Show that the algebraic closure of $F$ in $K$ is an algebraic closure of $F$.

Let $f(x)$ be an irreducible polynomial over $F$ of degree $n$, and let $K$ be a field extension of $F$ with $[K:F]=m$

Determine the splitting field of $x^4 - 7$ over

Extensions field in Galois Theory. Check Proof.

Let $\sigma \in\operatorname{Aut}(K)$ have infinite order and $F = \mathcal{F}(\sigma)$. Show that if $K/F$ is algebraic, then $K$ is normal over $F$.

degree/dimension of field extension if $K=\Bbb Q(\alpha)$ and $F=\Bbb Q$

Isomorphism between two extensions $\Bbb F_2(\alpha)$ and $\Bbb F_2(\beta)$

Galois extension over a field of characteristic $0$ of order $2^n$

Arguing that an extension is not normal

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