Weak Gamma (Quasi-) Continuous Modules
Ghassan Nieaf Abdulrazaq, Emad Allawi Shallal · Journal of Al-Qadisiyah for Computer Science and Mathematics · 2023
In this paper, we introduce and study the concept of weak gamma continuous modules as a generalization of continuous gamma modules. A gamma submodule of a gamma module is called weak gamma summand if there exists submodule of and there exists an ideal of where and . An module is called weak gamma extending module if every submodule of is essential in a weak gamma summand. An module is called weak gamma continuous module if is it weak gamma extending module and if for each submodule of is isomorphic to a direct summand of , then is weak gamma summand of . Also it is called weak gamma quasi-continuous module if is weak gamma extending module and if and are direct summands of with , then is a weak gamma summand of . Many properties and results of the these modules are given