Purely Goldie Extending Modules

Main Article Content

Saad A. Al-Saadi Ikbal A. Omer

Abstract

An -module  is extending if every submodule of   is essential in a direct summand of . Following Clark, an -module  is purely extending if every submodule of   is essential in a pure submodule of . It is clear purely extending is generalization of extending modules. Following Birkenmeier and Tercan, an -module     is Goldie extending if, for each submodule      of , there is a direct summand D of such that . In this paper, we introduce and study class of modules which are proper generalization of both the purely extending modules and -extending modules. We call an -module  is purely Goldie extending if, for each , there is a pure submodule P of such that  . Many characterizations and properties of purely Goldie extending modules are given. Also, we discuss when a direct sum of purely Goldie extending modules is purely Goldie extending and moreover we give a sufficient condition to make this property of purely  Goldie extending modules is valid. 

Article Details

How to Cite
AL-SAADI, Saad A.; OMER, Ikbal A.. Purely Goldie Extending Modules. Ibn AL- Haitham Journal For Pure and Applied Science, [S.l.], v. 28, n. 2, p. 147-154, mar. 2017. ISSN 2521-3407. Available at: <https://jih.uobaghdad.edu.iq/index.php/j/article/view/219>. Date accessed: 13 may 2021.
Section
mathematics