Question

If $[F(a):F]=5$, find $[F(a^3):F]$.

score 307 · Answer 1 · 2018-07-16 18:52:08

307

Views

If $[F(a):F]=5$, find $[F(a^3):F]$.

Published on 16 Jul 2018 - 18:52

score 176 · Answer 2 · 2018-07-17 10:51:58

176

Views

$\mathbb{Q}[\sqrt{2},\sqrt{3},\dots,\sqrt{n}]=\mathbb{Q}[\sqrt{2}+\sqrt{3}+\cdots+\sqrt{n}]$

Published on 17 Jul 2018 - 10:51

score 119 · Answer 3 · 2018-07-18 16:40:43

119

Views

Why is the "root field" premise necessary in this theorem about field extensions?

Published on 18 Jul 2018 - 16:40

score 87 · Answer 4 · 2026-03-22 23:31:58

87

Views

Creating new constants in differential field extensions via superfluous solutions to a D.E.

Published on 22 Mar 2026 - 23:31

score 328 · Answer 5 · 2026-03-25 14:30:00

328

Views

Irreducibility test in a number field

Published on 25 Mar 2026 - 14:30

score 35 · Answer 6 · 2018-07-19 20:29:38

35

Views

Let $K⊆M⊆L$, such that $[L:K]=n$ for some $n∈\mathbb{N}$. Prove $[M:K]$ is well-defined.

Published on 19 Jul 2018 - 20:29

score 50 · Answer 7 · 2018-07-21 19:53:54

50

Views

Constructing extension field $K_n$ of $\mathbb{Q}$ such that $[K_n : \mathbb{Q}] = n$, for any $n \geq 1$.

Published on 21 Jul 2018 - 19:53

score 980 · Answer 8 · 2018-07-23 12:50:36

980

Views

Express the inertia group in terms of the maximal unramified extension

Published on 23 Jul 2018 - 12:50

score 105 · Answer 9 · 2026-03-25 14:46:57

105

Views

Splitting field of a polynomial $f(x) =(x^2-3)(x^2-5)(x^5-1)$ over $\mathbb{Q}$.

Published on 25 Mar 2026 - 14:46

score 153 · Answer 10 · 2018-07-28 19:40:35

153

Views

Finding the norm map on number fields

Published on 28 Jul 2018 - 19:40

score 1.3k · Answer 11 · 2018-07-29 10:07:23

1.3k

Views

Degree of a field extension of a minimal polynomial

Published on 29 Jul 2018 - 10:07

score 51 · Answer 12 · 2018-07-30 18:39:11

51

Views

Absolute Galois groups for finite extensions

Published on 30 Jul 2018 - 18:39

score 276 · Answer 13 · 2018-07-31 14:23:54

276

Views

Field Extensions: Impossibility of trisecting an angle with compass and straightedge. Constructing arbitrary points?

Published on 31 Jul 2018 - 14:23

score 692 · Answer 14 · 2026-03-26 08:02:24

692

Views

On the proof of existence of algebraic closure using Zorn's Lemma in Patrick Morandi's Field and Galois Theory

Published on 26 Mar 2026 - 8:02

score 43 · Answer 15 · 2026-02-23 01:20:33

43

Views

An Upper and Lower Bound for a Field Extension of $\mathbb{Q}$ by a Complex Root

Published on 23 Feb 2026 - 1:20

List Question

If $[F(a):F]=5$, find $[F(a^3):F]$.

$\mathbb{Q}[\sqrt{2},\sqrt{3},\dots,\sqrt{n}]=\mathbb{Q}[\sqrt{2}+\sqrt{3}+\cdots+\sqrt{n}]$

Why is the "root field" premise necessary in this theorem about field extensions?

Creating new constants in differential field extensions via superfluous solutions to a D.E.

Irreducibility test in a number field

Let $K⊆M⊆L$, such that $[L:K]=n$ for some $n∈\mathbb{N}$. Prove $[M:K]$ is well-defined.

Constructing extension field $K_n$ of $\mathbb{Q}$ such that $[K_n : \mathbb{Q}] = n$, for any $n \geq 1$.

Express the inertia group in terms of the maximal unramified extension

Splitting field of a polynomial $f(x) =(x^2-3)(x^2-5)(x^5-1)$ over $\mathbb{Q}$.

Finding the norm map on number fields

Degree of a field extension of a minimal polynomial

Absolute Galois groups for finite extensions

Field Extensions: Impossibility of trisecting an angle with compass and straightedge. Constructing arbitrary points?

On the proof of existence of algebraic closure using Zorn's Lemma in Patrick Morandi's Field and Galois Theory

An Upper and Lower Bound for a Field Extension of $\mathbb{Q}$ by a Complex Root

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