The maximum condition on annihilators for polynomial rings
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- by Ferran Cedó and Dolors Herbera PDF
- Proc. Amer. Math. Soc. 126 (1998), 2541-2548 Request permission
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.References
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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
- 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
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2541-2548
- MSC (1991): Primary 16P60, 13B25
- DOI: https://doi.org/10.1090/S0002-9939-98-04321-4
- MathSciNet review: 1451790