We introduce a notion of CS-Rickart module being a modular analog of the ACS-ring concept. We describe the rings over which each finitely generated projective module is CS-Rickart module. The presented results yield the ...
Given an arbitrary quasiprojective right R-module P, we prove that every module in the category σ(P) is weakly regular if and only if every module in σ(M/I(M)) is lifting, where M is a generating object in σ(P). In particular, ...
We study rings over which every module is an I*0 -module dual to I 0-module. We describe semiregular rings over which every module is at the same time I*0 -module and I 0-module. We give a description of rings over which ...
The weakly regularity of all right R-modules with R an arbitrary ring does not imply the same property of all left R-modules. We describe the rings over which every right and left module is weakly regular and also obtain ...