Some results on nil-injective rings

Abstract

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 R_R  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  R_R 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.