Note on colon-multiplication domains
type: Item
instance of: scholarly article
title: Note on colon-multiplication domains
zbMATH Open document ID: 1197.13004
DOI: 10.1155/2010/231326
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2010-09-28T00:00:00Z
full work available at URL: https://eudml.org/doc/226114
review text: Summary: Let \(R\) be an integral domain with quotient field \(L\). Call a nonzero (fractional) ideal \(A\) of \(R\) a colon-multiplication ideal any ideal \(A\), such that \(B(A:B)=A\) for every nonzero (fractional) ideal \(B\) of \(R\). In this note, we characterize integral domains for which every maximal ideal (resp., every nonzero ideal) is a colon-multiplication ideal. It turns that this notion unifies Dedekind and MTP domains.
Mathematics Subject Classification ID: 13A15
zbMATH DE Number: 5792468
Wikidata QID: Q58651715
author: A. Mimouni
MaRDI profile type: Publication
OpenAlex ID: W2133858312
cites work: Q5661989
cites work: Q5603302
cites work: The radical trace property
cites work: Domains satisfying the trace property
cites work: Multiplication Ideals, Multiplication Rings, and the Ring R(X)
cites work: A Note on Finitely Generated Ideals which are Locally Principal
DBLP publication ID: journals/ijmmsc/Mimouni10
description: scientific article; zbMATH DE number 5792468