Newbetuts

Number of solns of $x^6+x=a$ in $\mathbb{F}_{2^m}$, where $m\geq 3$ is odd is same as number of solns of $x^2+ax+1=0$

$f$ is solvable by radicals, but the splitting field $L:Q$ not radical extension.

A basis of a field extension contained in a subring

Is a completion of an algebraically closed field with respect to a norm also algebraically closed?

Reducibility of $P(X^2)$

$\bar{\mathbb{F}}_p$ is not a finite degree extension of any proper subfield.

If $[K(\alpha):K]=p\neq q=[K(\beta):K]$ then $[K(\alpha+\beta):K]=pq$

The angle $168^\circ$ is constructible

The maximal unramified extension of a local field may not be complete

Why is a variety over a non-alg. closed field a hypersurface?

How to prove that if $\sigma\in \operatorname{Gal}(k(x)/k)\Leftrightarrow \sigma(x)=\frac{ax+b}{cx+d}$? [duplicate]

Is $\mathbb{Q}[\sqrt{2},\sqrt{3}]$ the same as $\mathbb{Q}(\sqrt{2},\sqrt{3})$?

Capelli Lemma for polynomials

Infinite algebraic extension of $\mathbb{Q}$

$[L:K]=n!\ \Longrightarrow \ f$ is irreducible and $\text{Gal}(L/K)\cong S_n.$

If $F=K(u,v)$ with $u^p$,$v^p\in K$ and $[F:K]=p^2$, $\operatorname{char} K=p>0$, then $F$ is not a simple extension of $K$.

New posts in field-theory

How to compute the Galois group of $x^5+99x-1$ over $\mathbb{Q}$?

Why don't these different factorizations of $7$ contradict number ring is UFD?

What is the difference between field theory and Galois theory

Rational function field over uncountable field is uncountably dimensional

Number of solns of $x^6+x=a$ in $\mathbb{F}_{2^m}$, where $m\geq 3$ is odd is same as number of solns of $x^2+ax+1=0$

$f$ is solvable by radicals, but the splitting field $L:Q$ not radical extension.

A basis of a field extension contained in a subring

Is a completion of an algebraically closed field with respect to a norm also algebraically closed?

Reducibility of $P(X^2)$

$\bar{\mathbb{F}}_p$ is not a finite degree extension of any proper subfield.

If $[K(\alpha):K]=p\neq q=[K(\beta):K]$ then $[K(\alpha+\beta):K]=pq$

The angle $168^\circ$ is constructible

The maximal unramified extension of a local field may not be complete

Why is a variety over a non-alg. closed field a hypersurface?

How to prove that if $\sigma\in \operatorname{Gal}(k(x)/k)\Leftrightarrow \sigma(x)=\frac{ax+b}{cx+d}$? [duplicate]

Is $\mathbb{Q}[\sqrt{2},\sqrt{3}]$ the same as $\mathbb{Q}(\sqrt{2},\sqrt{3})$?

Capelli Lemma for polynomials

Infinite algebraic extension of $\mathbb{Q}$

$[L:K]=n!\ \Longrightarrow \ f$ is irreducible and $\text{Gal}(L/K)\cong S_n.$

If $F=K(u,v)$ with $u^p$,$v^p\in K$ and $[F:K]=p^2$, $\operatorname{char} K=p>0$, then $F$ is not a simple extension of $K$.