On a radical extension of the field of rational functions in several variables
On a radical extension of the field of rational functions in several variables
Let F be a field and let F(X1,…,Xn) be the field of rational functions in n variables X1,…,Xn over F. Let T=X1+⋯+Xn∈F(X1,…,Xn) and let m be a positive integer such that charF∤m. Is it possible to express each Xi as a rational function in X1m…,Xnm and T over F? It …