Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

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?)

  • 1. D. Eisenbud and E. Graham Evans, Jr., Every Algebraic Set in n-Space is the Intersection of n Hypersufaces, Inventiones Math. 19 (1973), 107-112. MR 48:6125
  • 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 16D30, 16S36, 12E05

Retrieve articles in all journals with MSC (1991): 16D30, 16S36, 12E05

Additional Information

Miguel Ferrero
Affiliation: Instituto de Matemática, Universidade Federal do Rio Grande do Sul, 91509-900, Porto Alegre, Brazil

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

American Mathematical Society