Cofinitely weak generalized $\delta$-supplemented modules
چکیده
We will study modules whose cofinite submodules have weak generalized-$\delta$-supplements. We attempt to investigate some properties of cofinitely weak generalized $\delta$-supplemented modules. We will prove for a module $M$ and a semi-$\delta$-hollow submodule $N$ of $M$ that, $M$ is cofinitely weak generalized $\delta$-supplemented if and only if $\frac{M}{N}$ is cofinitely weak generalized $\delta$-supplemented. Also we show that any $M$-generated module is cofinitely weak generalized $\delta$-supplemented module, where $M$ is cofinitely weak generalized $\delta$-supplemented. We obtain some other results about this kind of modules.We will study modules whose cofinite submodules have weak generalized-$\delta$-supplements. We attempt to investigate some properties of cofinitely weak generalized $\delta$-supplemented modules. We will prove for a module $M$ and a semi-$\delta$-hollow submodule $N$ of $M$ that, $M$ is cofinitely weak generalized $\delta$-supplemented if and only if $\frac{M}{N}$ is cofinitely weak generalized $\delta$-supplemented. Also we show that any $M$-generated module is cofinitely weak generalized $\delta$-supplemented module, where $M$ is cofinitely weak generalized $\delta$-supplemented. We obtain some other results about this kind of modules.
