ON GENERALIZATION OF INJECTIVE MODULES

Abstract

Here we introduce the concept of CK-N-injectivity as a gen-eralization of N-injectivity. We give a homomorphism diagram representation of such concept, as well as an equivalent condition in terms of module decompositions. The concept CK-N-jectivity is also dealt with, as a generalization of CK-N-injectivity. We introduce a generalization of N-injectivity, namely C-N-injectivity. Its generalization CI-N-injectivity (given in [8] as C-N-injectivity).In our study of C-N-injectivity, we discovered some mistake results (given in [1]as IC-Pseudo-injecyivity), and we dealt with their corrections. Finally we turn our attention to a more generalization of injective modules, namely the generalized extending modules (or module with (C₁* )) and obtained some important results.