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