List questions from field-theory

Published on 11 Apr 2026 - 8:17

319

Views

Showing that if $E/F$ is a radical extension over $F$, then there is a radical tower where each extension is a simple radical extension of prime type.

Published on 13 Apr 2026 - 21:05

642

Views

$A$ algebra of finite type over $\mathbb{Z}$, $\mathfrak{m}$ max ideal implies $A/\mathfrak{m}$ is a finite field?

Published on 15 Apr 2026 - 19:43

64

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Field fixed by a given aut group

Published on 16 Apr 2026 - 23:27

492

Views

Show that a certain Extension is Simple (Lang, Algebra, Chapter 5, Problem 25)

Published on 15 Apr 2026 - 19:24

272

Views

Extension field definition vs Kronecker's theorem

Published on 13 Apr 2026 - 16:51

149

Views

Definition of an extension field question

Published on 16 Apr 2026 - 16:09

986

Views

Residue field degrees for number fields

Published on 14 Apr 2026 - 14:56

676

Views

$K$ field of characteristic $p$, where $p$ is prime

Published on 15 Apr 2026 - 0:59

81

Views

What does $\mathbb{F}_2[x] / (x^2+ 1)$ mean?

Published on 18 Apr 2026 - 16:26

67

Views

ordered field and R can embed

Published on 14 Apr 2026 - 19:15

45

Views

Prove that there's no order in the elements of $\Bbb{Z}_p$ where $p$ is prime

Published on 15 Apr 2026 - 16:36

60

Views

How would I go about factorising this into irreducibles in $\mathbb{Q}$

Published on 11 Apr 2026 - 20:17

78

Views

Is $\mathbb{R^+}$ a field?

Published on 11 Apr 2026 - 19:23

517

Views

How can I find the sum and multiplication table of a $F_4$ field?

Published on 13 Apr 2026 - 8:35

List Question

How to prove polynomials with degree $n$ does not form a vector space?

Showing that if $E/F$ is a radical extension over $F$, then there is a radical tower where each extension is a simple radical extension of prime type.

$A$ algebra of finite type over $\mathbb{Z}$, $\mathfrak{m}$ max ideal implies $A/\mathfrak{m}$ is a finite field?

Field fixed by a given aut group

Show that a certain Extension is Simple (Lang, Algebra, Chapter 5, Problem 25)

Extension field definition vs Kronecker's theorem

Definition of an extension field question

Residue field degrees for number fields

$K$ field of characteristic $p$, where $p$ is prime

What does $\mathbb{F}_2[x] / (x^2+ 1)$ mean?

ordered field and R can embed

Prove that there's no order in the elements of $\Bbb{Z}_p$ where $p$ is prime

How would I go about factorising this into irreducibles in $\mathbb{Q}$

Is $\mathbb{R^+}$ a field?

How can I find the sum and multiplication table of a $F_4$ field?

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