International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 90868, 6 pages
doi:10.1155/IJMMS/2006/90868
On n-flat modules and n-Von Neumann regular rings
Département de Mathématiques et Informatique, Faculté des Sciences et Techniques Fès-Saïss, Université S. M. Ben Abdellah, Fès BP 2202, Morocco
Received 4 May 2006; Revised 20 June 2006; Accepted 21 August 2006
Copyright © 2006 Najib Mahdou. 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
We show that each R-module is n-flat (resp., weakly n-flat) if and only if R is an (n,n−1)-ring (resp., a weakly (n,n−1)-ring). We also give a new characterization of n-Von Neumann regular rings and a characterization of weak n-Von Neumann regular rings for (CH)-rings and for local rings. Finally, we show that in a class of principal rings and a class of local Gaussian rings, a weak n-Von Neumann regular ring is a (CH)-ring.