A note on the birational cancellation problem
Journal
Journal of Pure and Applied Algebra
Journal Volume
77
Journal Issue
2
Pages
141-154
Date Issued
1992
Author(s)
Abstract
Let k be any field, K1 and K2 finitely generated extension fields of k, K1(x1,...,xn) and K2(y1,...,yn) the rational function fields of n variables over K1 and K2, respectively. Suppose that σ: K1(x1,...,xn)→K2(y1,...,yn) is a k-isomorphism of K1(x1,...,xn) onto K2(y1,...,yn). Theorem A. If σ(xi)=yi for 1≤i≤n, k is infinite and Autk (K1) is finite, then σ(K1)=K2. Theorem B. (1) If K1 has no proper k-endomorphism, then K1 is k-isomorphic to K2. (2) If Autk(K1) is finite and K1 has no proper k-endomorphism, then σ(K1)=K2. © 1992.
Type
journal article