论文信息 - MODULES THAT HAVE A WEAK SUPPLEMENT IN EVERY EXTENSION

MODULES THAT HAVE A WEAK SUPPLEMENT IN EVERY EXTENSION

We say that over an arbitrary ring a module M has the property (CWE) (respectively, (CWEE)) if M has a weak supplement (respectively, ample weak supplements) in every cofinite extension. We show that if every submodule of a module M has the property (CWE) then M has the property (CWEE). A ring R is semilocal iff every left R-module has the property (CWE). We also prove that over a commutative Von-Neumann regular ringR, anR-module M has the property (CWE) iff M is cofinitely injective.

H. Çalışıcı | E. Türkmen | E. Önal

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