AL-Rafidain Journal of Computer Sciences and Mathematics

A ring  is called right SNF-rings if every simple right R-module is N-flat . In this paper , we give some conditions which are sufficient or equivalent for a right SNF-ring to be n-regular (reduced) .It is shown that
1- If is a GW-ideal of R for every . then ,is reduced if and only if is right SNF-ring.
2- If  is an reversible, then  is regular if and only if  is right GQ-injective and SSNF-ring .
 

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.