Modules that have a Rad-supplement in every cofinite extension

WOS: 000338514500029 In this paper, we study modules with the properties (CRE) and (CREE), which are adapted Zoschinger's modules with the properties (E) and (EE). It is shown that: (1) a module M has the propery (CREE) if and only if every submodule of M has the propery (CRE); (2) a ring R is Rad-supplemented if and only if every left R-module has the propery (CRE); (3) over a commutative Von Neumann regular ring a module M has the propery (CRE) if and only if M is cofinitely injective.