Rad-Discrete Modules

We introduce Rad-discrete and quasi-Rad-discrete modules as a proper generalization of (quasi) discrete modules, and provide various properties of these modules. We prove that a direct summand of a (quasi) Rad-discrete module is (quasi) Rad-discrete. We show that every projective R-module is (quasi) Rad-discrete if and only if R is left perfect. We also prove that, over a commutative Noetherian ring R, every quasi-Rad-discrete R-module is the direct sum of local R-modules if and only if R is Artinian. Finally, we investigate self-projective Rad-discrete modules and π-projective quasi-Rad-discrete modules over Dedekind domains.