Question

Difficulties proving these two inequalities

score 29 · Answer 1 · 2015-09-17 13:20:13

29

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Difficulties proving these two inequalities

Published on 17 Sep 2015 - 13:20

score 571 · Answer 2 · 2015-09-17 19:16:58

571

Views

Why is extension of degree $2$ always _Galois_ $?$

Published on 17 Sep 2015 - 19:16

score 1k · Answer 3 · 2015-09-17 23:37:59

1k

Views

showing that two simple field extensions of $\mathbb{Q}$ are not isomorphic

Published on 17 Sep 2015 - 23:37

score 778 · Answer 4 · 2026-03-27 23:57:36

778

Views

Normal extensions and conjugates

Published on 27 Mar 2026 - 23:57

score 82 · Answer 5 · 2026-04-11 08:55:52

82

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The action of a subgroup of a Galois Group

Published on 11 Apr 2026 - 8:55

score 159 · Answer 6 · 2026-04-05 22:35:50

159

Views

Is $t^3+t+1$ irreducible over $\mathbb{Q}(\sqrt{-31})$?

Published on 05 Apr 2026 - 22:35

score 521 · Answer 7 · 2015-09-26 08:57:16

521

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the smallest normal extension of separable extension is separable.

Published on 26 Sep 2015 - 8:57

score 274 · Answer 8 · 2026-04-11 19:27:56

274

Views

Is there a smaller extension field than the algebraic closure which satisfy that every polynomial in it splits

Published on 11 Apr 2026 - 19:27

score 291 · Answer 9 · 2026-04-09 22:25:06

291

Views

Extending field homomorphisms in the general setting

Published on 09 Apr 2026 - 22:25

score 88 · Answer 10 · 2015-09-27 03:38:51

88

Views

The normal closure of $\mathbb{Q}(\alpha)$ with degree a power of 2 is in $\mathbb{R}$

Published on 27 Sep 2015 - 3:38

score 442 · Answer 11 · 2015-09-28 20:11:33

442

Views

If $a$ , $b$ have the same minimal polynomial there exists a field automorphism such that $\sigma(a)=b$

Published on 28 Sep 2015 - 20:11

score 112 · Answer 12 · 2026-04-08 19:11:08

112

Views

Let $K$ be a field. Prove that $K(X,Y)$ is a finite extension of $K(X^2,Y^2)$ and find its degree.

Published on 08 Apr 2026 - 19:11

score 62 · Answer 13 · 2026-04-11 16:45:46

62

Views

Degree of field extension with arbitrary algebraic elements

Published on 11 Apr 2026 - 16:45

score 157 · Answer 14 · 2015-10-02 18:26:02

157

Views

Prove $\sin(\alpha/n)$ and $\cos(\alpha/n)$ are algebraic over $K=\mathbb{Q}(\sin\alpha)$ for any positive integer $n$.

Published on 02 Oct 2015 - 18:26

score 71 · Answer 15 · 2015-10-03 19:54:13

71

Views

Find the degree of a finite field extension

Published on 03 Oct 2015 - 19:54

List Question

Difficulties proving these two inequalities

Why is extension of degree $2$ always _Galois_ $?$

showing that two simple field extensions of $\mathbb{Q}$ are not isomorphic

Normal extensions and conjugates

The action of a subgroup of a Galois Group

Is $t^3+t+1$ irreducible over $\mathbb{Q}(\sqrt{-31})$?

the smallest normal extension of separable extension is separable.

Is there a smaller extension field than the algebraic closure which satisfy that every polynomial in it splits

Extending field homomorphisms in the general setting

The normal closure of $\mathbb{Q}(\alpha)$ with degree a power of 2 is in $\mathbb{R}$

If $a$ , $b$ have the same minimal polynomial there exists a field automorphism such that $\sigma(a)=b$

Let $K$ be a field. Prove that $K(X,Y)$ is a finite extension of $K(X^2,Y^2)$ and find its degree.

Degree of field extension with arbitrary algebraic elements

Prove $\sin(\alpha/n)$ and $\cos(\alpha/n)$ are algebraic over $K=\mathbb{Q}(\sin\alpha)$ for any positive integer $n$.

Find the degree of a finite field extension

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