Weak Relative Injective M-Subgenerated Modules

We study weak relative injective and relative tight modules in the category σ [ M ], where М is a right R-module. Many of the known results in the category of right R-modules are extended to σ [ М ]without assuming either М is projective or finitely generated. Conditions are given for a A -tight module to be weakly A -injective in σ [ M ] . Modules for which every submodule is weakly injective (tight) in σ [ М ] are characterized. Modules М for which every module in σ [ М ] is weakly injective and for which weakly injective modules are closed under direct sums are studied. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.