Abstract
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.
Original language | English |
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Pages (from-to) | 2541-2548 |
Journal | Proceedings of the American Mathematical Society |
Volume | 126 |
Issue number | 9 |
Publication status | Published - 1 Dec 1998 |