On a radical extension of the field of rational functions in several variables

Xiang-dong Hou, Christopher Sze

Let $F$ be a field and let $F(X_1,\dots ,X_n)$ be the field of rational functions in $n$ variables $X_1,\dots ,X_n$ over $F$. Let $T=X_1+\cdots +X_n\in F(X_1,\dots ,X_n)$ and let $m$ b…