Prime ideals in polynomial rings
in several indeterminates
Proc. Amer. Math. Soc. 125 (1997), 67-74
Primary 16D30, 16S36; Secondary 12E05
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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.
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
Ferrero, Prime and principal closed ideals in polynomial
rings, J. Algebra 134 (1990), no. 1,
1068414 (91h:16008), http://dx.doi.org/10.1016/0021-8693(90)90210-F
M. Ferrero, Prime and Maximal Ideals in Polynomial Rings, Glasgow Math. J. 37 (1995), 351-362.
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
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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
This research was supported by a grant given by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil
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American Mathematical Society