Keywords : weakly continuous rings


On Generalized Simple Singular AP-Injective Rings

Raida D. Mahmood; Husam Q. Mohammad

AL-Rafidain Journal of Computer Sciences and Mathematics, 2012, Volume 9, Issue 1, Pages 175-180
DOI: 10.33899/csmj.2012.163681

A ring R is said to be generalized right simple singular AP-injective, if for any maximal essential right ideal M of R and for any bÎM, bR/bM is AP-injective. We shall study the characterization and properties of  this class of rings. Some interesting results on these rings are obtained. In particular, conditions under  which generalized simple singular AP-injective  rings are weakly regular rings, and Von Neumann regular rings.
 

On N–Flat Rings

Raida D. Mahmood; Husam Q. Mohammad

AL-Rafidain Journal of Computer Sciences and Mathematics, 2011, Volume 8, Issue 1, Pages 71-77
DOI: 10.33899/csmj.2011.163609

Let I be a right ideal of R, then R / I is a right N–flat if and only if for each a Î I, there exists b Î I and a positive integer n such that an ≠ 0 and an = ban. In this paper, we first give and develop various properties of right N-flat rings, by which, many of the known results are extended. Also, we study the relations between such rings and regular, p-biregular ring.