Question

Simple extension of a countable field is also countable?

score 1k · Answer 1 · 2016-01-04 01:50:25

1k

Views

Simple extension of a countable field is also countable?

Published on 04 Jan 2016 - 1:50

score 1.2k · Answer 2 · 2016-01-05 02:09:19

1.2k

Views

If b is algebraic over F(a), and a is algebraic over F, then is b algebraic over F?

Published on 05 Jan 2016 - 2:09

score 89 · Answer 3 · 2026-04-06 08:44:54

89

Views

Which of the following field properties are correct?

Published on 06 Apr 2026 - 8:44

score 1.2k · Answer 4 · 2016-01-06 00:25:00

1.2k

Views

$\mathbb{Q}$-automorphisms of $\mathbb{Q}(\sqrt{2}, \sqrt{3}, \sqrt{5})$

Published on 06 Jan 2016 - 0:25

score 78 · Answer 5 · 2016-01-06 05:26:47

78

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If $\sqrt[3]{2}+\omega\in \Bbb{K}$, prove that $\sqrt[3]{2}\in \Bbb{K}$

Published on 06 Jan 2016 - 5:26

score 2k · Answer 6 · 2016-01-06 09:11:37

2k

Views

Show that the only subfields of $\mathbb{Q}(i, \sqrt{5})$ is $\mathbb{Q}, \mathbb{Q}(i),\mathbb{Q}(\sqrt{5}), \mathbb{Q}(i \sqrt{5})$ and itself?

Published on 06 Jan 2016 - 9:11

score 328 · Answer 7 · 2016-01-09 18:44:15

328

Views

Does $S = R \cap K$ of a field extension $K \subseteq L = Q(R)$ satisfy $Q(S) = K$?

Published on 09 Jan 2016 - 18:44

score 1.8k · Answer 8 · 2016-01-11 09:17:13

1.8k

Views

Prove that every finite extension field of $\Bbb R$ is either $\Bbb R$ itself or isomorphic to $\Bbb C$.

Published on 11 Jan 2016 - 9:17

score 162 · Answer 9 · 2016-01-11 12:56:53

162

Views

Prove that $\Bbb Z_2(\alpha)=\Bbb Z_2(\beta)$ .

Published on 11 Jan 2016 - 12:56

score 3.1k · Answer 10 · 2016-01-11 15:59:11

3.1k

Views

Show that a finite field of order $p^n$ has exactly one subfield of $p^m$ elements for each divisor $m$ of $n$.

Published on 11 Jan 2016 - 15:59

score 3.6k · Answer 11 · 2016-01-11 19:46:29

3.6k

Views

General technique for finding minimal polynomial?

Published on 11 Jan 2016 - 19:46

score 50 · Answer 12 · 2026-04-09 18:01:12

50

Views

Show that the set {${\alpha \in F_{5^6} | F_5(\alpha)=F_{5^6} }$} contains 15480 elements

Published on 09 Apr 2026 - 18:01

score 84 · Answer 13 · 2016-01-14 12:41:52

84

Views

Degree of a field extension with three elements

Published on 14 Jan 2016 - 12:41

score 594 · Answer 14 · 2026-03-28 03:30:47

594

Views

Splitting field of $x^2 +1 \;$ over $\mathbb Z_7 $

Published on 28 Mar 2026 - 3:30

score 68 · Answer 15 · 2016-01-17 18:01:58

68

Views

The Galois Field for the polynomial $x^3 - 2$.

Published on 17 Jan 2016 - 18:01

List Question

Simple extension of a countable field is also countable?

If b is algebraic over F(a), and a is algebraic over F, then is b algebraic over F?

Which of the following field properties are correct?

$\mathbb{Q}$-automorphisms of $\mathbb{Q}(\sqrt{2}, \sqrt{3}, \sqrt{5})$

If $\sqrt[3]{2}+\omega\in \Bbb{K}$, prove that $\sqrt[3]{2}\in \Bbb{K}$

Show that the only subfields of $\mathbb{Q}(i, \sqrt{5})$ is $\mathbb{Q}, \mathbb{Q}(i),\mathbb{Q}(\sqrt{5}), \mathbb{Q}(i \sqrt{5})$ and itself?

Does $S = R \cap K$ of a field extension $K \subseteq L = Q(R)$ satisfy $Q(S) = K$?

Prove that every finite extension field of $\Bbb R$ is either $\Bbb R$ itself or isomorphic to $\Bbb C$.

Prove that $\Bbb Z_2(\alpha)=\Bbb Z_2(\beta)$ .

Show that a finite field of order $p^n$ has exactly one subfield of $p^m$ elements for each divisor $m$ of $n$.

General technique for finding minimal polynomial?

Show that the set {${\alpha \in F_{5^6} | F_5(\alpha)=F_{5^6} }$} contains 15480 elements

Degree of a field extension with three elements

Splitting field of $x^2 +1 \;$ over $\mathbb Z_7 $

The Galois Field for the polynomial $x^3 - 2$.

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