Some results on nil-injective rings

Let R be a ring. A right R-module is called nil-injective if for any element w is belong to the set of nilpotent elements, and any right R-homomorphism can be extended to R to M. If RR is nil-injective, then R is called a right nil-injective ring. A right R-module is called Wnil-injective if for each non-zero nilpotent element w of R, there exists a positive integer n such that wn not zero that right R-homomorphism f:wnR to M can be extended to R to M. If RR is right Wnil-injective, then is called a right Wnil-injective ring. In the present work, we discuss some characterizations and properties of right nil-injective and Wnil-injective rings.