Ideals that are an irredundant union of principal ideals
type: Item
instance of: scholarly article
title: Ideals that are an irredundant union of principal ideals
zbMATH Open document ID: 1261.13001
author: Sangmin Chun
author: D. D. Anderson
publication date: 2012-12-07T00:00:00Z
review text: This paper investigates the representation of an ideal in a commutative ring as an irredundant of principal ideals. Theorem 1 provides necessary and sufficient condition in order an ideal of a ring \(R\) to be an irredundant union of principal ideals. Moreover, the authors show that each ideal of a ring \(R\) is an irredundant union of principal ideals if and only if \(R\) satisfies the ascending chain condition on principal ideals. Finally, Theorem 3 states that a prime ideal is an irredundant union of principal ideals if and only if it is a union of principal ideals generated by irreducible elements.
reviewed by: Driss Karim
Mathematics Subject Classification ID: 13A05
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13E99
Mathematics Subject Classification ID: 13F15
zbMATH DE Number: 6113993
zbMATH Keywords: ACCP
zbMATH Keywords: atomic ring
zbMATH Keywords: CK ring
zbMATH Keywords: irreducible element
zbMATH Keywords: irredundant union of principal ideals
zbMATH Keywords: weak CK ring
MaRDI profile type: Publication
full work available at URL: s12215-012-0081-7
OpenAlex ID: W2006575522
cites work: Q4184971
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DOI: 10.1007/S12215-012-0081-7
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 6113993