On a radical extension of the field of rational functions in several variables
Xiang‐dong Hou, Christopher Sze · Linear and Multilinear Algebra · 2022
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 is not difficult to prove that this can be done but it is another matter to show how this is done. We answer the above question affirmatively with a nonconstructive proof and a constructive proof.