ON ALMOST WN-INJECTIVE RINGS

Let r be a ring. let m_r be a module with s = end(m_r) .the module m is called almost wnil- injective (briefly right awn-injective ) if , for any 0 # a n(r) ,there exists n ≥1 and an s-submodule a x_a of m such that an a^n #0 and l_m(r_r(a^n))= ma^n + x_a^n as left s-modules .if r_r is almost wnil- injective , then we call r is right almost wnil-injective ring . in this paper ,we give some characterization and properties of almost wnil-injective rings .in particular , conditions under which right almost wnil-injective rings are n-regular rings and n-weakly regular rings are given .also we study rings whose simple singular right r-module are almost wnil-injective , it is proved that if r is a nci ring ,mc2 , whose every simple singular r-module is almost wnil-injective , then r is reduced .