Nonuniqueness of coefficient rings in a polynomial ring

Abstract

An example is given of commutative rings B, C with 1 such that Bd^C but B[t]^C[t], where t is an indeterminate.Several authors [1], [2], [3] have recently studied the question, if /?[]=C[] (B, C are commutative rings with 1, / is an indeterminate), does B^C follow?A simple counterexample is given below.