All Questions

I ran into this MSE question and would like to ask about its answer and plausible generalizations. The quoted MSE question asks if the following claim is true or false and why: Claim: Let $a,b,c \in \...

Let $k$ be a field, $R:=k[x_1, \cdots , x_n]$ and $\mathfrak m$ be a maximal ideal such that $R/\mathfrak m$ is a finite separable field extension of $k$. Consider the algebraic closure $\overline k$ ...

When a result is stated for the field of complex numbers it can usually be extended to a result for an algebraically closed field of characteristic zero. I would like to see a list of results that ...

Let $\sigma:L \longrightarrow L$ an automorphism of infinite order, where $L_0 \subset L$ is its fixed field. Let $R$ be a commutative subring of $L\{\sigma\}$. Let \begin{equation} \mathcal{R}=\...

We assume $K$ as a field of characteristic zero. By a field of algebraic functions of one variable over $K$ we mean a field $R$ satisfying $R=K(x,y)$ with $x$ being transcendental over $K$, and $R$ is ...