Question

Determine all subfields of $\mathbb{Q}(\alpha)$, where $\alpha$ is real fourth root of $2$

score 227 · Answer 1 · 2026-04-15 18:22:02

227

Views

Determine all subfields of $\mathbb{Q}(\alpha)$, where $\alpha$ is real fourth root of $2$

Published on 15 Apr 2026 - 18:22

score 146 · Answer 2 · 2026-04-08 17:20:45

146

Views

Nilpotent Groups in Galois Theory?

Published on 08 Apr 2026 - 17:20

score 80 · Answer 3 · 2026-04-13 01:39:07

80

Views

Show that these two field extensions are equal and find the minimal polynomial

Published on 13 Apr 2026 - 1:39

score 67 · Answer 4 · 2026-04-12 10:22:49

67

Views

Understanding an example of a discrete valuation ring

Published on 12 Apr 2026 - 10:22

score 210 · Answer 5 · 2026-04-13 01:07:37

210

Views

Extensions of the field $k((x))$ of Laurent series

Published on 13 Apr 2026 - 1:07

score 67 · Answer 6 · 2026-04-15 18:43:38

67

Views

$p$-adic extension of $\mathbb{Q}_3$

Published on 15 Apr 2026 - 18:43

score 130 · Answer 7 · 2026-04-16 20:51:07

130

Views

Easy algebraic construction of $\overline{\mathbb Q}$?

Published on 16 Apr 2026 - 20:51

score 125 · Answer 8 · 2026-04-13 17:04:01

125

Views

Is there a name for a radical field extension of the rationals that contains all radical/solvable elements?

Published on 13 Apr 2026 - 17:04

score 30 · Answer 9 · 2026-04-15 16:47:01

30

Views

$(r+1)^{\frac{1}{3}}$ transcendental and $s^2-s$ algebraic on $\mathbb{Q}$ then $r$ is transcendental and $s$ algebraic on $\mathbb{Q}$

Published on 15 Apr 2026 - 16:47

score 185 · Answer 10 · 2026-04-11 08:45:10

185

Views

Finite and Infinite Field Extensions of Complex

Published on 11 Apr 2026 - 8:45

score 39 · Answer 11 · 2026-04-10 21:39:17

39

Views

Is a scalar extension of an $(t)$-adically complete module complete?

Published on 10 Apr 2026 - 21:39

score 212 · Answer 12 · 2026-04-17 14:04:58

212

Views

The Galois group $Gal(\mathbb{Q}[\sqrt{p_1}, \dots , \sqrt{p_n}] | \mathbb{Q})$, $p_1, \dots , p_n$ prime integers, has $2^n-1$ subgroups of index $2$

Published on 17 Apr 2026 - 14:04

score 534 · Answer 13 · 2026-04-15 01:07:00

534

Views

Show $\alpha$ is separable over a field $F$ iff $F(\alpha) = F(\alpha^p)$.

Published on 15 Apr 2026 - 1:07

score 60 · Answer 14 · 2026-04-16 18:12:22

60

Views

The splitting field on $\mathbb{Q}$ of $x^4+10x^2+5$ is $\mathbb{Q}[i\sqrt{5-2\sqrt{5}}]$

Published on 16 Apr 2026 - 18:12

score 256 · Answer 15 · 2026-04-15 23:35:13

256

Views

Prove that there exists an infinite field $F$ such that $F$ is algebraic over a finite field, and $F$ is not algebraically closed

Published on 15 Apr 2026 - 23:35

List Question

Determine all subfields of $\mathbb{Q}(\alpha)$, where $\alpha$ is real fourth root of $2$

Nilpotent Groups in Galois Theory?

Show that these two field extensions are equal and find the minimal polynomial

Understanding an example of a discrete valuation ring

Extensions of the field $k((x))$ of Laurent series

$p$-adic extension of $\mathbb{Q}_3$

Easy algebraic construction of $\overline{\mathbb Q}$?

Is there a name for a radical field extension of the rationals that contains all radical/solvable elements?

$(r+1)^{\frac{1}{3}}$ transcendental and $s^2-s$ algebraic on $\mathbb{Q}$ then $r$ is transcendental and $s$ algebraic on $\mathbb{Q}$

Finite and Infinite Field Extensions of Complex

Is a scalar extension of an $(t)$-adically complete module complete?

The Galois group $Gal(\mathbb{Q}[\sqrt{p_1}, \dots , \sqrt{p_n}] | \mathbb{Q})$, $p_1, \dots , p_n$ prime integers, has $2^n-1$ subgroups of index $2$

Show $\alpha$ is separable over a field $F$ iff $F(\alpha) = F(\alpha^p)$.

The splitting field on $\mathbb{Q}$ of $x^4+10x^2+5$ is $\mathbb{Q}[i\sqrt{5-2\sqrt{5}}]$

Prove that there exists an infinite field $F$ such that $F$ is algebraic over a finite field, and $F$ is not algebraically closed

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