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 | References | Similar Articles | Additional Information

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

**1.**David Eisenbud and E. Graham Evans Jr.,*Every algebraic set in 𝑛-space is the intersection of 𝑛 hypersurfaces*, Invent. Math.**19**(1973), 107–112. MR**0327783****2.**Miguel Ferrero,*Prime and principal closed ideals in polynomial rings*, J. Algebra**134**(1990), no. 1, 45–59. MR**1068414**, 10.1016/0021-8693(90)90210-F**3.**M. Ferrero,*Prime and Maximal Ideals in Polynomial Rings*, Glasgow Math. J. 37 (1995), 351-362.**4.**Irving Kaplansky,*Commutative rings*, Revised edition, The University of Chicago Press, Chicago, Ill.-London, 1974. MR**0345945**

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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

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