Chains of factorizations and sets of lengths
type: Item
instance of: scholarly article
title: Chains of factorizations and sets of lengths
zbMATH Open document ID: 0882.20039
author: Alfred Geroldinger
published in: Journal of Algebra
publication date: 1998-03-09T00:00:00Z
review text: In the theory of nonunique factorization in integral domains, a crucial invariant is the set of lengths of factorizations. If \(R\) is a Krull domain with finite divisor class group, then sets of lengths are almost arithmetical progressions. This paper investigates chains of factorizations and sets of lengths in the setting of weakly Krull monoids. The main result (for domains) is that for a Noetherian weakly Krull domain \(R\) with finite \(t\)-class group and whose integral closure is a finite \(R\)-module, there is a positive integer \(C\) such that for all nonzero nonunits \(a\) of \(R\) and each two factorizations \(z\) and \(z'\) of \(a\), there is a \(C\)-chain of factorizations from \(z\) to \(z'\) whose lengths form an almost arithmetical progression.
Mathematics Subject Classification ID: 20M14
Mathematics Subject Classification ID: 13G05
Mathematics Subject Classification ID: 13F99
Mathematics Subject Classification ID: 11R27
zbMATH DE Number: 1013927
zbMATH Keywords: nonunique factorizations in integral domains
zbMATH Keywords: lengths of factorizations
zbMATH Keywords: Krull domains
zbMATH Keywords: divisor class groups
zbMATH Keywords: sets of lengths
zbMATH Keywords: almost arithmetical progressions
zbMATH Keywords: chains of factorizations
zbMATH Keywords: weakly Krull monoids
zbMATH Keywords: nonunits
reviewed by: David F. Anderson
MaRDI profile type: Publication
full work available at URL: jabr.1996.6838
OpenAlex ID: W2020370373
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DOI: 10.1006/JABR.1996.6838
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description: scientific article; zbMATH DE number 1013927