AL-Rafidain Journal of Computer Sciences and Mathematics

The ring R is called right almost weakly np –injective, if for any , there exists a positive integer n and a left ideal  of R such that . In this paper, we give some characterization and properties of almost weakly np – injective rings. And we study the regularity of right almost weakly np – injective ring and in the same time, when every simple (simple singular) right R – module is almost weakly np – injective, we also give some properties of an R.
 

Let I be a right (left) ideal of a ring R. Then R/I is a right (left) generalized m – flat modules (GmF – module) if and only if for each , there exist  and a fixed positive integer m such that . We study characterization and properties this class of flat modules, and we give the relation between this class and generalized m- flat modules and m – regular rings, reduced rings, reversible rings and uniform rings.
 

In this work, we study rings whose every principal ideal is a right pure. We give some properties of right PIP – rings and the connection between such rings and division rings.
 

In this work we consider weakly regular rings whose simple singular right R-Modules are flat. We also consider the condition (*): R satisfies L(a)Ír(a) for any aÎR. We prove that if R satisfies(*) and whose simple singular right R-module are flat, then Z (R)  the center of  R  is a von    Neunann regular ring. We also show that a ring R either satisfies (*) or a strongly right bounded ring in which every simple singular right R-module is flat, then  R is reduced weakly regular rings.