THE MAXIMUM CONDITION ON ANNIHILATORS FOR POLYNOMIAL-RINGS

For each positive integer n, we construct a commutative ring R such th at the polynomial ring R[x(1),...,x(n)] satisfies the maximum conditio n on annihilators and R[x(1),..., x(n+1)] does not. In particular, the re exists a commutative Kerr ring R such that R[x] is not Kerr. This a nswers in the negative a question of Faith's.