Modules That Have a Weak delta-Supplement in Every Cofinite Extension

Abstract

In this paper, we study on modules that have a weak (ample) delta-supplement in every extension which are adapted Zoschinger's modules with the properties (E) and (EE). It is shown that: (1) Direct summands of modules with the property delta-(CWE) have the property delta-(CWE); (2) For a module M, if every submodule of M has the property delta-(CWE) then so does M; (3) For a ring R, R is delta-semilocal iff every R-module has the property delta-(CWE); (4) Every factor module of a finitely generated module that has the property delta-(CWE) also has the property delta-(CWE)under a special condition; (5) Let M be a module and L be a submodule of M such that L <<(delta) M. If the factor module M/L has the property delta-(CWE), then so does M; (6) On a semisimple module the concepts of modules that have the property delta-(CE) and delta-(CWE) coincide with each other.