Factorization in integral domains without identity
type: Item
instance of: scholarly article
title: Factorization in integral domains without identity
zbMATH Open document ID: 1197.13003
author: Jonathan Preisser
author: D. D. Anderson
published in: Results in Mathematics
publication date: 2010-01-18T00:00:00Z
review text: The aim of this paper is to study factorization in a nonzero commutative integral domain \(A\) without identity. Considering \(A\) as a proper ideal of an integral domain \(D\) with identity having the same quotient field \(K\) as \(A\), with \(A[1]\subseteq D \subseteq A:A\), where \(1\) is the identity element of \(K\) and \(A:A = \{\,x\in K\,|\,xA \subseteq A\,\}\), the author investigates the relationship between factorization in \(A\) and \(D\), mainly when \(D=A[1]\) or \(D= A:A\). Thus, various generalizations of unique factorization are studied in \(A\), as well as the relationship between the property of \(A\) or \(D\) being atomic, or a bounded factorization domain, or a half-factorial domain, or a finite factorization domain, or satisfying the ACC on principal ideals, etc.
Mathematics Subject Classification ID: 13A05
Mathematics Subject Classification ID: 13B99
Mathematics Subject Classification ID: 13F15
Mathematics Subject Classification ID: 13G05
zbMATH DE Number: 5659727
zbMATH Keywords: ACCP
zbMATH Keywords: atomic domain
zbMATH Keywords: bounded factorization domain
zbMATH Keywords: finite factorization domain
zbMATH Keywords: half-factorial domain
zbMATH Keywords: integral domain without identity
zbMATH Keywords: unique factorization
reviewed by: Toma Albu
MaRDI profile type: Publication
full work available at URL: s00025-009-0405-x
OpenAlex ID: W2040543413
DOI: 10.1007/S00025-009-0405-X
description: scientific article; zbMATH DE number 5659727