Question

Field Extension $ \mathbb{Q} \subset \mathbb{Q}_p $ infinite

score 98 · Answer 1 · 2026-03-26 19:37:48

98

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Field Extension $ \mathbb{Q} \subset \mathbb{Q}_p $ infinite

Published on 26 Mar 2026 - 19:37

score 86 · Answer 2 · 2019-04-16 03:27:11

86

Views

$\mathbb{Q}(\alpha)\cap\mathbb{R}=\mathbb{Q}$, where $\alpha=\sqrt{\frac{3+\sqrt{7}i}{2}}$

Published on 16 Apr 2019 - 3:27

score 946 · Answer 3 · 2019-04-16 16:15:40

946

Views

Simplicity of the roots of a minimal polynomial

Published on 16 Apr 2019 - 16:15

score 119 · Answer 4 · 2019-04-16 23:07:35

119

Views

How to find the basis of an extension field

Published on 16 Apr 2019 - 23:07

score 183 · Answer 5 · 2019-04-16 23:57:45

183

Views

minimal polynomial for $\sqrt{-3}+\sqrt{2}$ over $\mathbb{Q}$

Published on 16 Apr 2019 - 23:57

score 143 · Answer 6 · 2019-04-17 00:39:46

143

Views

Show that there exists an $\alpha \in K$ such that $\alpha^2 \in F$ but $\alpha \notin F$

Published on 17 Apr 2019 - 0:39

score 125 · Answer 7 · 2026-03-25 22:30:12

125

Views

Tower of Splitting Fields

Published on 25 Mar 2026 - 22:30

score 60 · Answer 8 · 2019-04-17 20:00:27

60

Views

Let $F = \mathbb{Q}(a_1, a_2, . . . , a_n)$ with $a_i^2 \in \mathbb{Q}.$ Prove that $ \sqrt[3]2 \notin F$.

Published on 17 Apr 2019 - 20:00

score 167 · Answer 9 · 2026-03-28 17:42:00

167

Views

Factorization of a polynomial in $\Bbb F_7$

Published on 28 Mar 2026 - 17:42

score 242 · Answer 10 · 2026-03-25 06:04:41

242

Views

What is the Galois group of the Hyperreal Numbers?

Published on 25 Mar 2026 - 6:04

score 64 · Answer 11 · 2026-03-25 23:58:39

64

Views

For a field $K$ of characteristics $p>0$, when is a finite purely inseparable extension $F/K$ (with $[F:K]=p^n>1$) such that $F\cong K$?

Published on 25 Mar 2026 - 23:58

score 499 · Answer 12 · 2026-03-25 22:26:08

499

Views

When degree of splitting field equals n factorial

Published on 25 Mar 2026 - 22:26

score 82 · Answer 13 · 2019-04-20 20:20:54

82

Views

Prove that $[E(u): F(u)] \leq [E:F]$.

Published on 20 Apr 2019 - 20:20

score 175 · Answer 14 · 2026-02-23 03:01:17

175

Views

If $x$ and $y$ are complex numbers and $x+y$ , $xy$ are algebraic numbers then how to prove that $x$ and $y$ are also algebraic numbers?

Published on 23 Feb 2026 - 3:01

score 323 · Answer 15 · 2019-04-21 18:15:33

323

Views

Find degree of extension $Q$($\sqrt{1+\sqrt{-3}}$ + $\sqrt{1-\sqrt{-3}}$) over $Q$

Published on 21 Apr 2019 - 18:15

List Question

Field Extension $ \mathbb{Q} \subset \mathbb{Q}_p $ infinite

$\mathbb{Q}(\alpha)\cap\mathbb{R}=\mathbb{Q}$, where $\alpha=\sqrt{\frac{3+\sqrt{7}i}{2}}$

Simplicity of the roots of a minimal polynomial

How to find the basis of an extension field

minimal polynomial for $\sqrt{-3}+\sqrt{2}$ over $\mathbb{Q}$

Show that there exists an $\alpha \in K$ such that $\alpha^2 \in F$ but $\alpha \notin F$

Tower of Splitting Fields

Let $F = \mathbb{Q}(a_1, a_2, . . . , a_n)$ with $a_i^2 \in \mathbb{Q}.$ Prove that $ \sqrt[3]2 \notin F$.

Factorization of a polynomial in $\Bbb F_7$

What is the Galois group of the Hyperreal Numbers?

For a field $K$ of characteristics $p>0$, when is a finite purely inseparable extension $F/K$ (with $[F:K]=p^n>1$) such that $F\cong K$?

When degree of splitting field equals n factorial

Prove that $[E(u): F(u)] \leq [E:F]$.

If $x$ and $y$ are complex numbers and $x+y$ , $xy$ are algebraic numbers then how to prove that $x$ and $y$ are also algebraic numbers?

Find degree of extension $Q$($\sqrt{1+\sqrt{-3}}$ + $\sqrt{1-\sqrt{-3}}$) over $Q$

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