Question

How do I show that $\alpha$ is not an element of $F(\beta)$

score 30 · Answer 1 · 2026-03-25 23:38:44

30

Views

How do I show that $\alpha$ is not an element of $F(\beta)$

Published on 25 Mar 2026 - 23:38

score 31 · Answer 2 · 2018-10-08 14:32:53

31

Views

Show that extension is simple

Published on 08 Oct 2018 - 14:32

score 305 · Answer 3 · 2018-10-09 13:15:43

305

Views

Basis of finite Galois extension generated by Galois group acting on single element.

Published on 09 Oct 2018 - 13:15

score 46 · Answer 4 · 2018-10-10 10:15:08

46

Views

Shared properties of several extensions of $\mathbb{Z}$

Published on 10 Oct 2018 - 10:15

score 136 · Answer 5 · 2026-03-25 16:20:51

136

Views

Find the condition on $a, b$ such that the field of $x^3+ax+b\in\Bbb{Q}[x]$ has degree of extension 6.

Published on 25 Mar 2026 - 16:20

score 222 · Answer 6 · 2026-03-26 23:11:14

222

Views

Can one find intermediate subextensions of a finite cyclic field extension whose degrees are prime powers?

Published on 26 Mar 2026 - 23:11

score 28 · Answer 7 · 2018-10-11 00:30:35

28

Views

How to show the degree of every factor of unique factorization of $f(x)$ over $L$ is 1?

Published on 11 Oct 2018 - 0:30

score 52 · Answer 8 · 2026-03-25 16:13:50

52

Views

Showing that the splitting fields of $x^{2^m}+1$ and $x^{2^{m+1}}-1$ over $\mathbb{F}_p$ are isomorphic.

Published on 25 Mar 2026 - 16:13

score 61 · Answer 9 · 2018-10-12 07:23:05

61

Views

Simple extensions of $\mathbb{Z}$ by rational numbers

Published on 12 Oct 2018 - 7:23

score 54 · Answer 10 · 2018-10-13 15:19:15

54

Views

Verify the proof about field extension.

Published on 13 Oct 2018 - 15:19

score 46 · Answer 11 · 2026-03-26 04:53:03

46

Views

About roots of unity in an arbitrary CM field K with an abelian extension L

Published on 26 Mar 2026 - 4:53

score 77 · Answer 12 · 2018-10-15 12:06:13

77

Views

Does there exist at least an extension of $\sigma$ to an embedding of $E$ in $L$?

Published on 15 Oct 2018 - 12:06

score 1.1k · Answer 13 · 2018-10-15 13:59:13

1.1k

Views

$\mathbb{Q}(\alpha)=\mathbb{Q}(\beta)$ if $\alpha, \beta$ are algebraic over $\mathbb{Q}$ of degree $2$ and $\alpha +\beta$ is a root of a quadratic.

Published on 15 Oct 2018 - 13:59

score 121 · Answer 14 · 2018-10-15 16:21:06

121

Views

How to show the set $\operatorname{Hom}_K(L,\bar{K})$ of all $K$-embeddings of $L$ is partitioned into $m$ equivalence classes of $d$ elements each?

Published on 15 Oct 2018 - 16:21

score 131 · Answer 15 · 2018-10-15 23:26:51

131

Views

On the number of embeddings in algebraic closure.

Published on 15 Oct 2018 - 23:26

List Question

How do I show that $\alpha$ is not an element of $F(\beta)$

Show that extension is simple

Basis of finite Galois extension generated by Galois group acting on single element.

Shared properties of several extensions of $\mathbb{Z}$

Find the condition on $a, b$ such that the field of $x^3+ax+b\in\Bbb{Q}[x]$ has degree of extension 6.

Can one find intermediate subextensions of a finite cyclic field extension whose degrees are prime powers?

How to show the degree of every factor of unique factorization of $f(x)$ over $L$ is 1?

Showing that the splitting fields of $x^{2^m}+1$ and $x^{2^{m+1}}-1$ over $\mathbb{F}_p$ are isomorphic.

Simple extensions of $\mathbb{Z}$ by rational numbers

Verify the proof about field extension.

About roots of unity in an arbitrary CM field K with an abelian extension L

Does there exist at least an extension of $\sigma$ to an embedding of $E$ in $L$?

$\mathbb{Q}(\alpha)=\mathbb{Q}(\beta)$ if $\alpha, \beta$ are algebraic over $\mathbb{Q}$ of degree $2$ and $\alpha +\beta$ is a root of a quadratic.

How to show the set $\operatorname{Hom}_K(L,\bar{K})$ of all $K$-embeddings of $L$ is partitioned into $m$ equivalence classes of $d$ elements each?

On the number of embeddings in algebraic closure.

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