List questions from field-theory

Published on 11 Apr 2026 - 20:13

362

Views

How to prove that $k(x)$ is not complete in the $x$-adic metric

Published on 17 Apr 2026 - 11:27

146

Views

Showing that a Polynomial is Irreducible Over $\mathbb{Z}_3$

Published on 11 Apr 2026 - 21:53

110

Views

$\Bbb Q(\sqrt{12},i)$ is a simple extension of $\Bbb Q $

Published on 16 Apr 2026 - 16:01

49

Views

To what extent is $\textbf{Fld}$ not a filtered category?

Published on 17 Apr 2026 - 13:06

105

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Why is a field $\mathbb{F}$ "always" chosen as $\mathbb{R}, \mathbb{C}$?

Published on 17 Apr 2026 - 13:14

45

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What can I deduce from the char a of a field?

Published on 12 Apr 2026 - 12:28

72

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Valuation of a root smaller than valuation of a polynomial

Published on 13 Apr 2026 - 10:36

93

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Proving that $\sum\limits_{a\in \Bbb{F}_q^\times} a^k=0$ for $k\not\equiv 0\mod q-1$

Published on 16 Apr 2026 - 2:54

59

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What is the generator of the fraction field of $K(y)[T]/(T^2-1-y^2)$?

Published on 12 Apr 2026 - 0:44

281

Views

what is $\mathbb{Q}(i) \otimes \mathbb{R}$?

Published on 13 Apr 2026 - 22:35

137

Views

Proof in field theory

Published on 09 Apr 2026 - 19:27

110

Views

What is the relationship between Cyclotomic Field Extensions and Circles?

Published on 10 Apr 2026 - 6:52

45

Views

What is the name of this concept in algebra?

Published on 11 Apr 2026 - 23:06

315

Views

A basis of a Galois extension.

Published on 13 Apr 2026 - 19:52

List Question

Division algebra = Field?

How to prove that $k(x)$ is not complete in the $x$-adic metric

Showing that a Polynomial is Irreducible Over $\mathbb{Z}_3$

$\Bbb Q(\sqrt{12},i)$ is a simple extension of $\Bbb Q $

To what extent is $\textbf{Fld}$ not a filtered category?

Why is a field $\mathbb{F}$ "always" chosen as $\mathbb{R}, \mathbb{C}$?

What can I deduce from the char a of a field?

Valuation of a root smaller than valuation of a polynomial

Proving that $\sum\limits_{a\in \Bbb{F}_q^\times} a^k=0$ for $k\not\equiv 0\mod q-1$

What is the generator of the fraction field of $K(y)[T]/(T^2-1-y^2)$?

what is $\mathbb{Q}(i) \otimes \mathbb{R}$?

Proof in field theory

What is the relationship between Cyclotomic Field Extensions and Circles?

What is the name of this concept in algebra?

A basis of a Galois extension.

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