The maximum condition on annihilators for polynomial rings

For each positive integer n, we construct a commutative ring R such that the polynomial ring R: [xi,... ,xn] satisfies the maximum condition on annihilators and R [x1,... ,xn+i] does not. In particular, there exists a commutative Kerr ring R. such that R [x] is not Kerr. This answers in the negative a question of Faith's. ©1998 American Mathematical Society.