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In this paper, we study modules with the properties (CRE) and (CREE), which are adapted Zöschinger’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. 2010 Mathematics Subject Classification: 16D10; 16N80

Modules that have a Rad-supplement in every cofinite extension