Cofinitely weak generalized $\delta$-supplemented modules

Document Type : Research Paper

Author

Department of Math. Faculty of Basic Science, Babol Noshirvani University of technology, Babol, Iran

10.29252/as.2020.1620

Abstract

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.

Keywords


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