List questions from field-theory

Published on 09 Apr 2026 - 20:12

53

Views

Show that $n$ is a divisor of $[L:K]$

Published on 14 Apr 2026 - 8:28

432

Views

Integral closure of Gaussian Integers

Published on 25 Mar 2026 - 4:39

155

Views

Show that $K(a_1, \dots , a_n)=K[a_1, \dots , a_n]$

Published on 17 Apr 2026 - 10:29

265

Views

Is it true that $\mathbb{Q}(\sqrt{2},e^{2i\pi/3}) = \mathbb{Q}(\sqrt{2}+e^{2i\pi/3})$?

Published on 15 Apr 2026 - 5:23

1.4k

Views

Does there exist any isomorphism between $\mathbb Q[\sqrt 2]$ and $\mathbb Q[\sqrt 3]$?

Published on 15 Apr 2026 - 22:06

126

Views

Why is analysis over the complex numbers so useful vs say other fields?

Published on 17 Apr 2026 - 2:14

293

Views

Solvability and reducibility of a polynomial in a "chain" of finite fields

Published on 13 Apr 2026 - 5:44

626

Views

A question concerning non-algebraic extension.

Published on 14 Apr 2026 - 6:20

54

Views

What does a finite extension look like?

Published on 11 Apr 2026 - 11:35

281

Views

Ring->module->$R$-algebra, Field->Vectorspace->algebra

Published on 14 Apr 2026 - 21:15

6k

Views

Non-trivial example of algebraically closed fields

Published on 13 Apr 2026 - 21:06

144

Views

Affine group, $[L : \mathbb{Q}] = n\varphi(n)$ or ${1\over2}n\varphi(n)$

Published on 17 Apr 2026 - 8:48

116

Views

Is $x^{2\cdot 3^n}+x^{3^n}+1$ irreducible (mod 2)?

Published on 15 Apr 2026 - 11:42

273

Views

Is there an infinite field F with char(F)=p and not algebraically closed field?

Published on 16 Apr 2026 - 16:56

List Question

Show that $[L:K]=1 \Leftrightarrow L=K$

Show that $n$ is a divisor of $[L:K]$

Integral closure of Gaussian Integers

Show that $K(a_1, \dots , a_n)=K[a_1, \dots , a_n]$

Is it true that $\mathbb{Q}(\sqrt{2},e^{2i\pi/3}) = \mathbb{Q}(\sqrt{2}+e^{2i\pi/3})$?

Does there exist any isomorphism between $\mathbb Q[\sqrt 2]$ and $\mathbb Q[\sqrt 3]$?

Why is analysis over the complex numbers so useful vs say other fields?

Solvability and reducibility of a polynomial in a "chain" of finite fields

A question concerning non-algebraic extension.

What does a finite extension look like?

Ring->module->$R$-algebra, Field->Vectorspace->algebra

Non-trivial example of algebraically closed fields

Affine group, $[L : \mathbb{Q}] = n\varphi(n)$ or ${1\over2}n\varphi(n)$

Is $x^{2\cdot 3^n}+x^{3^n}+1$ irreducible (mod 2)?

Is there an infinite field F with char(F)=p and not algebraically closed field?

Trending Questions

Popular # Hahtags

Popular Questions