MMN-1496
On cofinitely weak $\delta-$ supplemented modules
Figen Eryilmaz; Senol Eren;Abstract
Let $R$ be a ring and $M$ be a left $R-$module. $M$ is called \textit{%
cofinitely weak } $\delta -$\textit{supplemented} (or briefly $\delta -$%
\textit{CWS}-module) if every cofinite submodule of $M$ has a weak $\delta -$%
supplement in $M$. In this paper, we give various properties of this kind of
modules. It is shown that a module $M$ is $\delta -$\textit{CWS}-module if
and only if every maximal submodule has a weak $\delta -$supplement in $M$.
The class of cofinitely weak $\delta -$supplemented modules are closed under
taking homomorphic images, arbitrary sums and short exact sequences. Also we
give some conditions equivalent to being a $\delta -$\textit{CWS}-module for
a $\delta -$coatomic module.
Vol. 18 (2017), No. 2, pp. 731-738