The distribution of prime divisors in Krull monoid domains
type: Item
instance of: scholarly article
title: The distribution of prime divisors in Krull monoid domains
zbMATH Open document ID: 0971.13015
DOI: 10.1016/S0022-4049(99)00105-X
author: Hwankoo Kim
published in: Journal of Pure and Applied Algebra
publication date: 2001-06-21T00:00:00Z
review text: It is well-known that each divisor class of a Krull domain \(D\) contains a height-one prime ideal if either \(D\) is a ring of algebraic integers or \(D\) is a polynomial ring \(R[X]\) where of course \(R\) is a Krull domain. In this paper it is shown that if the monoid domain \(R[S]\) is a Krull domain \((S\) is a torsion-free cancellative monoid) and either \(R\) is a UFD (but not a field) or \(S\) is a group, then each divisor class of \(R[S]\) contains a height-one prime.
Mathematics Subject Classification ID: 13F05
Mathematics Subject Classification ID: 13C20
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13F15
Mathematics Subject Classification ID: 13G05
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 13A05
zbMATH DE Number: 1563013
zbMATH Keywords: divisor class
zbMATH Keywords: Krull domain
zbMATH Keywords: monoid domain
reviewed by: D. D. Anderson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1563013