Question

Given $F_0\subset\cdots\subset F_n$ and intermediate $E$, finding $F=E_0\subset\cdots\subset E_m=E$ such that $\max[E_i:E_{i-1}]\le\max[F_i:F_{i-1}]$

score 33 · Answer 1 · 2023-11-25 21:42:01

33

Views

Given $F_0\subset\cdots\subset F_n$ and intermediate $E$, finding $F=E_0\subset\cdots\subset E_m=E$ such that $\max[E_i:E_{i-1}]\le\max[F_i:F_{i-1}]$

Published on 25 Nov 2023 - 21:42

score 111 · Answer 2 · 2023-11-27 20:51:02

Let $F$ be a field with characteristic 0, and $p(x)\in F[x]$ be an irreducible polynomial of degree 3 with root $\alpha$. Show $F(\alpha)=F(\alpha^2)$

score 72 · Answer 3 · 2023-11-29 12:16:30

72

Views

How can I determine if a class is a set

Published on 29 Nov 2023 - 12:16

score 50 · Answer 4 · 2026-03-25 17:52:01

50

Views

Construct precisely the cyclotomic extension of $\mathbf{Q}$

Published on 25 Mar 2026 - 17:52

score 67 · Answer 5 · 2023-11-29 21:36:17

67

Views

$F(a_1,\ldots,a_{n-1})(a_n)=F(a_1,\ldots,a_n)$

Published on 29 Nov 2023 - 21:36

score 59 · Answer 6 · 2023-11-30 08:23:55

59

Views

Showing that field embedding exists

Published on 30 Nov 2023 - 8:23

score 36 · Answer 7 · 2026-03-27 17:04:19

36

Views

Question about the degree of the splitting field of $X^4-2X^2-2$

Published on 27 Mar 2026 - 17:04

score 49 · Answer 8 · 2026-03-26 22:13:40

49

Views

Analytic equivalence and isomorphism of valued fields

Published on 26 Mar 2026 - 22:13

score 62 · Answer 9 · 2026-03-27 20:31:38

62

Views

$E := \mathbb{Q}( \sqrt{3}, \sqrt{5}, \sqrt[3]{7})/ \mathbb{Q}$. Determine a $ϑ ∈ E$ with $E = \mathbb{Q}(ϑ)$.

Published on 27 Mar 2026 - 20:31

score 68 · Answer 10 · 2026-03-27 15:36:19

68

Views

An exercise where I need to prove that a field extension is normal

Published on 27 Mar 2026 - 15:36

score 109 · Answer 11 · 2026-03-27 17:06:20

109

Views

Exercises on the field extension $E := \mathbb{F}_3[X]/(X^2 + X + 2)$

Published on 27 Mar 2026 - 17:06

score 39 · Answer 12 · 2026-03-29 11:06:58

39

Views

Exercises about Galois theory and isomorphism type of the Galois-Group

Published on 29 Mar 2026 - 11:06

score 49 · Answer 13 · 2026-04-08 09:24:00

49

Views

Some exercises about field extensions and galois groups

Published on 08 Apr 2026 - 9:24

score 46 · Answer 14 · 2026-04-07 20:06:09

46

Views

How could I formalize this field extensions problem?

Published on 07 Apr 2026 - 20:06

score 66 · Answer 15 · 2026-03-29 11:07:00

66

Views

Some exercises about Galois Groups and Automorphisms of a finite field extension

Published on 29 Mar 2026 - 11:07

List Question

Given $F_0\subset\cdots\subset F_n$ and intermediate $E$, finding $F=E_0\subset\cdots\subset E_m=E$ such that $\max[E_i:E_{i-1}]\le\max[F_i:F_{i-1}]$

Let $F$ be a field with characteristic 0, and $p(x)\in F[x]$ be an irreducible polynomial of degree 3 with root $\alpha$. Show $F(\alpha)=F(\alpha^2)$

How can I determine if a class is a set

Construct precisely the cyclotomic extension of $\mathbf{Q}$

$F(a_1,\ldots,a_{n-1})(a_n)=F(a_1,\ldots,a_n)$

Showing that field embedding exists

Question about the degree of the splitting field of $X^4-2X^2-2$

Analytic equivalence and isomorphism of valued fields

$E := \mathbb{Q}( \sqrt{3}, \sqrt{5}, \sqrt[3]{7})/ \mathbb{Q}$. Determine a $ϑ ∈ E$ with $E = \mathbb{Q}(ϑ)$.

An exercise where I need to prove that a field extension is normal

Exercises on the field extension $E := \mathbb{F}_3[X]/(X^2 + X + 2)$

Exercises about Galois theory and isomorphism type of the Galois-Group

Some exercises about field extensions and galois groups

How could I formalize this field extensions problem?

Some exercises about Galois Groups and Automorphisms of a finite field extension

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