List questions from field-theory

Published on 14 Apr 2026 - 19:12

139

Views

Primitive field

Published on 13 Apr 2026 - 2:01

75

Views

Equivalent criterion for algebraic independence over $\mathbb{Q}$.

Published on 26 Mar 2026 - 19:27

172

Views

An exercise about fields extensions

Published on 11 Apr 2026 - 7:25

104

Views

What is the extension of function fields corresponding to the Artin-Schreier isogeny?

Published on 11 Apr 2026 - 22:24

315

Views

If $\Sigma $ is the splitting field of $f$ over $K$ and $K \subseteq L \subseteq \Sigma$, show that $\Sigma$ is the splitting field of $f$ over $L$.

Published on 15 Apr 2026 - 4:03

886

Views

$K[x]$ is an integral domain, a subring of $L$ but not always a field

Published on 12 Apr 2026 - 22:41

239

Views

The largest field contained in $GL_2(\mathbb{R})$

Published on 12 Apr 2026 - 2:26

144

Views

Why is : $ \pi_1 ( X , \overline{x} ) = \mathrm{Gal} ( \overline{k} / k ) $?

Published on 15 Apr 2026 - 14:47

115

Views

How do I know a property is "algebraic"?

Published on 10 Apr 2026 - 19:35

46

Views

Counter-examples to $x \not \in K \implies \Bbb Q(x) \cap K = \Bbb Q$

Published on 16 Apr 2026 - 1:40

1.7k

Views

Prove that $F[a]$ is a field if and only if $a$ is algebraic over $F$

Published on 15 Apr 2026 - 15:07

107

Views

Is there any non trivial reflective subcategory of the category of fields?

Published on 16 Apr 2026 - 19:40

710

Views

A finite extension is simple iff the purely inseparable closure is simple?

Published on 15 Apr 2026 - 3:46

47

Views

For $f(x) = x^4 -x ^2 - 2 = (x^2-2)(x^2+1)$ in $\Bbb Q[x]$, show that $\Bbb Q(\sqrt{2}, i)$ is the splitting field.

Published on 17 Apr 2026 - 7:59

List Question

Factorizing minimal polynomials

Primitive field

Equivalent criterion for algebraic independence over $\mathbb{Q}$.

An exercise about fields extensions

What is the extension of function fields corresponding to the Artin-Schreier isogeny?

If $\Sigma $ is the splitting field of $f$ over $K$ and $K \subseteq L \subseteq \Sigma$, show that $\Sigma$ is the splitting field of $f$ over $L$.

$K[x]$ is an integral domain, a subring of $L$ but not always a field

The largest field contained in $GL_2(\mathbb{R})$

Why is : $ \pi_1 ( X , \overline{x} ) = \mathrm{Gal} ( \overline{k} / k ) $?

How do I know a property is "algebraic"?

Counter-examples to $x \not \in K \implies \Bbb Q(x) \cap K = \Bbb Q$

Prove that $F[a]$ is a field if and only if $a$ is algebraic over $F$

Is there any non trivial reflective subcategory of the category of fields?

A finite extension is simple iff the purely inseparable closure is simple?

For $f(x) = x^4 -x ^2 - 2 = (x^2-2)(x^2+1)$ in $\Bbb Q[x]$, show that $\Bbb Q(\sqrt{2}, i)$ is the splitting field.

Trending Questions

Popular # Hahtags

Popular Questions