Some Results on Regular Modules

In this pap er we st udy t he relati onship between t heproj ecti vity and regualari ty. we show that every pro jective moduleover a von neuman regular ring is regular . we also show thata projective module p is regular iff every cyclic submodule of p isa dir ect summand of p and we sha ll see that if p is a pr oj ectiveregular module t hen j(p) = z(p) = 0 where j (p ) and z( p) aret he j acobson and singular submodules of p resp ecti vely. also p isregular and indecomposable iff p is project ive and hollow. in thispaper r will be a commutat ive ring with identity and all modulesare unitary.