The maximum condition on annihilators for polynomial rings

Ferran Cedó; Dolors Herbera

The maximum condition on annihilators for polynomial rings

Ferran Cedó, Dolors Herbera

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

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

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title = "The maximum condition on annihilators for polynomial rings",

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. {\textcopyright}1998 American Mathematical Society.",

author = "Ferran Ced{\'o} and Dolors Herbera",

year = "1998",

month = dec,

day = "1",

language = "English",

volume = "126",

pages = "2541--2548",

number = "9",

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TY - JOUR

T1 - The maximum condition on annihilators for polynomial rings

AU - Cedó, Ferran

AU - Herbera, Dolors

PY - 1998/12/1

Y1 - 1998/12/1

N2 - 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.

AB - 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.

M3 - Article

VL - 126

SP - 2541

EP - 2548

IS - 9

ER -