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.
|Journal||Proceedings of the American Mathematical Society|
|Publication status||Published - 1 Dec 1998|