Question

What are all the subfields of $\mathbb Q(p^{\frac{1}{4}}, q^{\frac{1}{2}})$ for any two distinct primes $p,q$?

score 56 · Answer 1 · 2026-04-17 08:30:35

56

Views

What are all the subfields of $\mathbb Q(p^{\frac{1}{4}}, q^{\frac{1}{2}})$ for any two distinct primes $p,q$?

Published on 17 Apr 2026 - 8:30

score 30 · Answer 2 · 2026-04-09 19:43:00

30

Views

How to prove extension field question.

Published on 09 Apr 2026 - 19:43

score 40 · Answer 3 · 2026-04-17 08:15:07

40

Views

Find $p(x)\in \mathbb{K}(\alpha)[x]$ of degree 2 such that $p(\beta)=0$

Published on 17 Apr 2026 - 8:15

score 181 · Answer 4 · 2026-04-14 16:59:59

181

Views

Order of elements in the multiplicative group of the finite field extension

Published on 14 Apr 2026 - 16:59

score 177 · Answer 5 · 2026-04-17 11:05:28

177

Views

Find $Gal(\mathbb{Q}(e^{2\pi i/6},e^{2\pi i / 10}) / \mathbb{Q})$

Published on 17 Apr 2026 - 11:05

score 103 · Answer 6 · 2026-04-17 13:41:58

103

Views

Prove $\mathbb Q(t)/\mathbb Q(\frac{1-3t+t^3}{t(t-1)})$ is Galois with $G=\mathbb Z/3\mathbb Z$ and $\sigma t = \frac{1}{1-t} $

Published on 17 Apr 2026 - 13:41

score 136 · Answer 7 · 2026-04-09 12:16:52

136

Views

Do the subfields preserve unity?

Published on 09 Apr 2026 - 12:16

score 126 · Answer 8 · 2026-04-13 10:19:57

126

Views

Does $K(a,b)=K(a+b)$ hold?

Published on 13 Apr 2026 - 10:19

score 71 · Answer 9 · 2026-04-14 13:08:46

71

Views

Minimal vector space over a subfield that corresponds to a given vector

Published on 14 Apr 2026 - 13:08

score 294 · Answer 10 · 2026-04-14 14:40:57

294

Views

Is $\mathbb{Q}(\cos\frac{2\pi}{13})/\mathbb{Q}$ a Galois extension?

Published on 14 Apr 2026 - 14:40

score 117 · Answer 11 · 2026-04-16 06:42:37

117

Views

Minimal polynomial of $\sqrt[10]{5}$ over $\mathbb{Q}(e^{2\pi i/10})$

Published on 16 Apr 2026 - 6:42

score 33 · Answer 12 · 2026-04-16 15:50:29

33

Views

If $E|_k$ is a finite extension such that $E^pk=E$, then prove $E^{p^m}k=E$ where $p=$char$(k)$

Published on 16 Apr 2026 - 15:50

score 96 · Answer 13 · 2026-04-16 07:43:23

96

Views

Check whether $f(x)=x^5+10x^3+10x+3$ is irreducible over $\Bbb{Q}(i)$ or not.

Published on 16 Apr 2026 - 7:43

score 95 · Answer 14 · 2026-04-15 04:07:16

95

Views

Must an algebraically closed field be an algebraic closure of some field?

Published on 15 Apr 2026 - 4:07

score 43 · Answer 15 · 2026-04-14 11:58:37

43

Views

Field extension, is every element , algebraic over $\Bbb Q\bigl[\sqrt2\,\bigr]$, algebraic over $\Bbb Q$?

Published on 14 Apr 2026 - 11:58

List Question

What are all the subfields of $\mathbb Q(p^{\frac{1}{4}}, q^{\frac{1}{2}})$ for any two distinct primes $p,q$?

How to prove extension field question.

Find $p(x)\in \mathbb{K}(\alpha)[x]$ of degree 2 such that $p(\beta)=0$

Order of elements in the multiplicative group of the finite field extension

Find $Gal(\mathbb{Q}(e^{2\pi i/6},e^{2\pi i / 10}) / \mathbb{Q})$

Prove $\mathbb Q(t)/\mathbb Q(\frac{1-3t+t^3}{t(t-1)})$ is Galois with $G=\mathbb Z/3\mathbb Z$ and $\sigma t = \frac{1}{1-t} $

Do the subfields preserve unity?

Does $K(a,b)=K(a+b)$ hold?

Minimal vector space over a subfield that corresponds to a given vector

Is $\mathbb{Q}(\cos\frac{2\pi}{13})/\mathbb{Q}$ a Galois extension?

Minimal polynomial of $\sqrt[10]{5}$ over $\mathbb{Q}(e^{2\pi i/10})$

If $E|_k$ is a finite extension such that $E^pk=E$, then prove $E^{p^m}k=E$ where $p=$char$(k)$

Check whether $f(x)=x^5+10x^3+10x+3$ is irreducible over $\Bbb{Q}(i)$ or not.

Must an algebraically closed field be an algebraic closure of some field?

Field extension, is every element , algebraic over $\Bbb Q\bigl[\sqrt2\,\bigr]$, algebraic over $\Bbb Q$?

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