International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 231326, 4 pages
doi:10.1155/2010/231326
Research Article

Note on Colon-Multiplication Domains

A. Mimouni

Department of Mathematics and Statistics, King Fahd University of Petroleum & Minerals, P.O. Box 278, Dhahran 31261, Saudi Arabia

Received 8 April 2010; Accepted 25 August 2010

Academic Editor: David Dobbs

Copyright © 2010 A. Mimouni. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.