Weak Gamma (Quasi-) Continuous Modules
DOI:
https://doi.org/10.29304/jqcm.2023.15.2.1248Keywords:
Gamma module, weak gamma summand, weak continuous gamma module, weak quasi-continuous gamma module, weak gamma extending moduleAbstract
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
Downloads
References
[2] Ameri R and Sadeghi R, Gamma module, Ratio Mathematics, 20, (2010), 127-147.
[3]M.S. Abbas, S.A. Al-Saadi and E.A.Shallal , (Quasi-)Injective extending gamma modules, journal of Al-Qadisiyah for Computer Science and Mathematices, 9(2), (2017),71-80.
[4] N. Nobusawa, 1964, On a generalization of the ring theory, Osaka Journal Math., 1,pp. 81-89.
[5] E.A.Shallal, Idempotint extending modules, Journal of physics: Conference Series, 1664, (2020), 1-7.
[6] E.A.Shallal and G.N. Abdulrazaq , (Quasi-) Continuous gamma modules, An Interdisciplinary journal of Neuroscience and Quantum physics, 20, No 9 (2022).
[7] E.A.Shallal , A.T.Husseien and A.K.Lelo , Power gamma extending modules, Italian journal of pure and applied Mathematics – N.47-2022(950-957).
