Primary decomposition of divisorial ideals in Mori domains
type: Item
instance of: scholarly article
title: Primary decomposition of divisorial ideals in Mori domains
zbMATH Open document ID: 0675.13002
DOI: 10.1016/0021-8693(88)90110-X
author: Thomas G. Lucas
author: T. M. Viswanathan
author: Evan Houston
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: A Mori domain is an integral domain which satisfies the ascending chain condition on divisorial ideals. In general, a divisorial ideal in a Mori domain is neither a finite intersection of divisorial primary ideals nor a finite intersection of primary ideals in the usual sense. The notion of divisorial irreducibility for divisorial ideals is introduced and studied. Necessary and sufficient conditions for the existence of divisorial primary decompositions are given. Some special techniques are used to show that every divisorial ideal of a two dimensional Mori domain has a primary decomposition.
Mathematics Subject Classification ID: 13A05
Mathematics Subject Classification ID: 13E99
Mathematics Subject Classification ID: 13G05
Mathematics Subject Classification ID: 13A15
zbMATH DE Number: 4105091
zbMATH Keywords: Mori domain
zbMATH Keywords: ascending chain condition
zbMATH Keywords: divisorial irreducibility
zbMATH Keywords: divisorial primary decompositions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4105091