Properties of factorizations with successive lengths in one-dimensional local domains
type: Item
instance of: scholarly article
title: Properties of factorizations with successive lengths in one-dimensional local domains
zbMATH Open document ID: 1223.13001
DOI: 10.1216/JCA-2009-1-2-237
published in: Journal of Commutative Algebra
publication date: 2010-02-19T00:00:00Z
review text: Let \(D\) be a \(1\)-dimensional local domain whose integral closure is a finitely generated \(D\)-module and for non-unit \(a\in D\) denote by \(Z_n(a)\) the set of factorizations of \(a\) into irreducibles with length \(n\). The paper is devoted to an investigation of the structure of the sets \(Z_n(a)\). It is shown in particular that if integers \(k<l\) satisfy \(Z_k(a)\neq\emptyset\), \(Z_l(a)\neq\emptyset\), and the sets \(Z_j(a)\) are empty for \(k<j<l\), then in general \(Z_k(a)\) and \(Z_l(a)\) have a similar structure.
reviewed by: Władysław Narkiewicz
Mathematics Subject Classification ID: 13A05
Mathematics Subject Classification ID: 11R27
Mathematics Subject Classification ID: 13G05
Mathematics Subject Classification ID: 13H99
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 5673529
zbMATH Keywords: factorizations
zbMATH Keywords: local domains
zbMATH Keywords: factorization lengths
author: Wolfgang Hassler
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5673529