On cancellation of variables of the form bTn−abTn−a over affine normal domains

In this article we extend a cancellation theorem of D. Wright to the case of affine normal domains. We shall show that if A is an algebra over a Noetherian normal domain R containing a field k   and if A[T]=R[3]A[T]=R[3], then A=R[2]A=R[2] if and only if A[T]A[T] has a variable of the form bTn−abTn−a for some a,b∈Aa,b∈A with n≥2n≥2 and ch(k)∤nch(k)∤n.