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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Prime ideals in polynomial rings
in several indeterminates


Author: Miguel Ferrero
Journal: Proc. Amer. Math. Soc. 125 (1997), 67-74
MSC (1991): Primary 16D30, 16S36; Secondary 12E05
DOI: https://doi.org/10.1090/S0002-9939-97-03663-0
MathSciNet review: 1363458
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Abstract | References | Similar Articles | Additional Information

Abstract: If $P$ is a prime ideal of a polynomial ring $K[x]$, where $K$ is a field, then $P$ is determined by an irreducible polynomial in $K[x]$. The purpose of this paper is to show that any prime ideal of a polynomial ring in $n$-indeterminates over a not necessarily commutative ring $R$ is determined by its intersection with $R$ plus $n$ polynomials.


References [Enhancements On Off] (What's this?)

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  • 2. M. Ferrero, Prime and Principal Closed Ideals in Polynomial Rings, J. Algebra 134 (1990), 45-59. MR 91h:16008
  • 3. M. Ferrero, Prime and Maximal Ideals in Polynomial Rings, Glasgow Math. J. 37 (1995), 351-362.
  • 4. I. Kaplansky, Commutative Rings, The University of Chicago Press, Chicago (1974). MR 49:10674

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Additional Information

Miguel Ferrero
Affiliation: Instituto de Matemática, Universidade Federal do Rio Grande do Sul, 91509-900, Porto Alegre, Brazil
Email: Ferrero@if.ufrgs.br

DOI: https://doi.org/10.1090/S0002-9939-97-03663-0
Received by editor(s): March 15, 1995
Received by editor(s) in revised form: July 28, 1995
Additional Notes: This research was supported by a grant given by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil
Communicated by: Ken Goodearl
Article copyright: © Copyright 1997 American Mathematical Society

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