Question

Extending a finite field twice

score 133 · Answer 1 · 2026-04-09 14:27:53

133

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Extending a finite field twice

Published on 09 Apr 2026 - 14:27

score 256 · Answer 2 · 2014-05-24 09:44:29

256

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Integral closure of a subring that is a polynomial ring over an algebraically closed field.

Published on 24 May 2014 - 9:44

score 58 · Answer 3 · 2026-04-11 15:18:15

58

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How would do this Algebra question?

Published on 11 Apr 2026 - 15:18

score 1.1k · Answer 4 · 2026-04-03 14:57:29

1.1k

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Let $F/\mathbb{Q}$ be a degree 4 extension, NOT Galois. Prove that the Galois closure of $F$ has Galois group either $S_4, A_4$ or $D_8$.

Published on 03 Apr 2026 - 14:57

score 1.4k · Answer 5 · 2026-04-01 20:54:46

1.4k

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Galois group - extend homomorphism to automorphism

Published on 01 Apr 2026 - 20:54

score 1.5k · Answer 6 · 2026-04-03 14:52:49

1.5k

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Fixed Field of Automorphisms of $k(x)$

Published on 03 Apr 2026 - 14:52

score 1.4k · Answer 7 · 2014-05-26 01:39:28

1.4k

Views

Is there a specific method to finding a basis for vector spaces over $\mathbb{Q}$ ?

Published on 26 May 2014 - 1:39

score 200 · Answer 8 · 2026-04-11 12:19:45

200

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How exactly is $i=\sqrt{-1}$ related to $\mathbb{C}$ being a closed algebraic field?

Published on 11 Apr 2026 - 12:19

score 1.4k · Answer 9 · 2014-05-27 03:55:46

1.4k

Views

Field $K (x)$ of rational functions over $K$, the element $x$ has no $p$th root.

Published on 27 May 2014 - 3:55

score 2k · Answer 10 · 2026-03-25 22:26:43

2k

Views

When is a companion matrix diagonalizable and what does this say about the associated field extension?

Published on 25 Mar 2026 - 22:26

score 62 · Answer 11 · 2014-05-27 11:40:06

62

Views

Why does the characteristic need to be 3?

Published on 27 May 2014 - 11:40

score 85 · Answer 12 · 2026-03-27 22:52:49

85

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Why is $x^2-2ux+1$, where $u = \cos(\frac{2\pi}{n})$, irreducible in $\mathbb Q(u)$?

Published on 27 Mar 2026 - 22:52

score 76 · Answer 13 · 2026-04-01 20:53:18

76

Views

A result on extension fields in linear algebra.

Published on 01 Apr 2026 - 20:53

score 101 · Answer 14 · 2026-03-30 12:02:39

101

Views

Prove that $\alpha_{1} ^k+ \alpha_{2} ^k +.....+ \alpha_{n} ^k = n$ for $k=0$ and $0$ for $k = 1,2,....,n-1$?

Published on 30 Mar 2026 - 12:02

score 146 · Answer 15 · 2026-04-11 06:48:53

146

Views

Hilbert's Basis Theorem question

Published on 11 Apr 2026 - 6:48

List Question

Extending a finite field twice

Integral closure of a subring that is a polynomial ring over an algebraically closed field.

How would do this Algebra question?

Let $F/\mathbb{Q}$ be a degree 4 extension, NOT Galois. Prove that the Galois closure of $F$ has Galois group either $S_4, A_4$ or $D_8$.

Galois group - extend homomorphism to automorphism

Fixed Field of Automorphisms of $k(x)$

Is there a specific method to finding a basis for vector spaces over $\mathbb{Q}$ ?

How exactly is $i=\sqrt{-1}$ related to $\mathbb{C}$ being a closed algebraic field?

Field $K (x)$ of rational functions over $K$, the element $x$ has no $p$th root.

When is a companion matrix diagonalizable and what does this say about the associated field extension?

Why does the characteristic need to be 3?

Why is $x^2-2ux+1$, where $u = \cos(\frac{2\pi}{n})$, irreducible in $\mathbb Q(u)$?

A result on extension fields in linear algebra.

Prove that $\alpha_{1} ^k+ \alpha_{2} ^k +.....+ \alpha_{n} ^k = n$ for $k=0$ and $0$ for $k = 1,2,....,n-1$?

Hilbert's Basis Theorem question

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