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Proceedings of the American Mathematical Society
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
MathSciNet review: 1363458
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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.


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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: http://dx.doi.org/10.1090/S0002-9939-97-03663-0
PII: S 0002-9939(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