PRIME IDEALS IN POLYNOMIAL-RINGS OVER ONE-DIMENSIONAL DOMAINS

Authors
HEINZER W WIEGAND S
Citation
W. Heinzer et S. Wiegand, PRIME IDEALS IN POLYNOMIAL-RINGS OVER ONE-DIMENSIONAL DOMAINS, Transactions of the American Mathematical Society, 347(2), 1995, pp. 639-650
Citations number
13
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Transactions of the American Mathematical Society → ACNP
ISSN journal
00029947
Volume
347
Issue
2
Year of publication
1995
Pages
639 - 650
Database
ISI
SICI code
0002-9947(1995)347:2<639:PIIPOO>2.0.ZU;2-E
Abstract
Let R be a one-dimensional integral domain with only finitely many max imal ideals and let x be an indeterminate over R. We study the prime s pectrum of the polynomial ring R[x] as a partially ordered set. In the case where R is countable we classify Spec(R[x]) in terms of splittin g properties of the maximal ideals m of R and the valuative dimension of R(m).