On the integral closure of a half-factorial domain
type: Item
instance of: scholarly article
title: On the integral closure of a half-factorial domain
zbMATH Open document ID: 1031.13011
DOI: 10.1016/S0022-4049(02)00303-1
published in: Journal of Pure and Applied Algebra
publication date: 2003-04-28T00:00:00Z
review text: A half-factorial domain (HFD), \(R\), is an atomic integral domain where given any two products of irreducible elements of \(R\): \(\alpha_1 \alpha_2\dots \alpha_n= \beta_1\beta_2 \dots\beta_m\) then \(n=m\). As a natural generalization of unique factorization domains (UFD), one wishes to investigate which ``good'' properties of UFDs that HFDs possess. In particular, it has been conjectured that the integral closure of a half-domain is again a HFD [\textit{S. T. Chapman} and \textit{J. Coykendall} in: Non-Noetherian commutative ring theory, Math. Appl., Dordr. 520, 97-115 (2000; Zbl 0987.13010)]. In this paper we produce an example that demonstrates that the integral closure of a HDF does not even have to be atomic. We investigate the failure of this conjecture closely and highlight some cases where the conjecture does indeed hold.
Mathematics Subject Classification ID: 13F15
Mathematics Subject Classification ID: 13B22
Mathematics Subject Classification ID: 13F05
Mathematics Subject Classification ID: 13G05
zbMATH DE Number: 1901793
zbMATH Keywords: half-factorial domain
zbMATH Keywords: atomic integral domain
zbMATH Keywords: UFD
zbMATH Keywords: integral closure
author: Jim Coykendall
MaRDI profile type: Publication
cites work: A Characterization of Algebraic Number Fields with Class Number Two
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cites work: Q4343547
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cites work: Half factorial domains
cites work: Half-factorial-domains
description: scientific article; zbMATH DE number 1901793