Modules With Annihilator Conditions

Abstract

Let S and R be rings. The objective is to study the bimodule S N R satisfying the annihilator conditions l N ðr R ðxÞÞ ¼ Sx for all x 2 N. This approach will clearly show how the ring R or the module N R is connected to the properties of the ring S through the annhilator condition. Specializing to the particular bimodule R R R or End ðNÞN R , we obtain some new results and known results as corollaries.

ON NIL n-INJECTIVE RINGS

“…Generalizations of injectivity have been discussed in many papers(see [3], [4], [8]- [10], [11]- [14], [15]- [19]). A right R-module M is called principally injective (or P-injective), if every R-homomorphism from a principal right ideal of R to M can be extended to an R-homomorphism from R to M .…”