The maximum condition on annihilators for polynomial rings

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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 languageEnglish
Pages (from-to)2541-2548
JournalProceedings of the American Mathematical Society
Volume126
Issue number9
Publication statusPublished - 1 Dec 1998

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