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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The maximum condition on annihilators
for polynomial rings


Authors: Ferran Cedó and Dolors Herbera
Journal: Proc. Amer. Math. Soc. 126 (1998), 2541-2548
MSC (1991): Primary 16P60, 13B25
MathSciNet review: 1451790
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Abstract: For each positive integer $n$, we construct a commutative ring ${\mathcal{R}}$ such that the polynomial ring ${\mathcal{R}}[x_{1},\ldots ,x_{n}]$ satisfies the maximum condition on annihilators and ${\mathcal{R}}[x_{1},\ldots ,x_{n+1}]$ does not. In particular, there exists a commutative Kerr ring ${\mathcal{R}}$ such that ${\mathcal{R}}[x]$ is not Kerr. This answers in the negative a question of Faith's.


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Additional Information

Ferran Cedó
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
Email: cedo@mat.uab.es

Dolors Herbera
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
Email: dolors@mat.uab.es

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04321-4
PII: S 0002-9939(98)04321-4
Received by editor(s): May 10, 1996
Received by editor(s) in revised form: January 30, 1997
Additional Notes: Both authors are partially supported by the DGICYT (Spain), through the grant PB95-0626, and by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya.
Communicated by: Ken Goodearl
Article copyright: © Copyright 1998 American Mathematical Society