Purely goldie extending modules
Other Title(s)
مقاسات التوسع النقية من النمط-G
Joint Authors
Umar, Iqbal Ahmad
al-Saidi, Sad Abd al-Kazim
Source
Ibn al-Haitham Journal for Pure and Applied Science
Issue
Vol. 28, Issue 2 (31 Aug. 2015), pp.147-154, 8 p.
Publisher
University of Baghdad College of Education for Pure Science / Ibn al-Haitham
Publication Date
2015-08-31
Country of Publication
Iraq
No. of Pages
8
Main Subjects
Abstract EN
An R-module M is extending if every submodule of M is essential in a direct summand of M.
Following Clark, an R-module M is purely extending if every submodule of M is essential in a pure submodule of M.
It is clear purely extending is generalization of extending modules.
Following Birkenmeier and Tercan, an R-module M is Goldie extending if, for each submodule X of M, there is a direct summand D of Msuch that X β D.
In this paper, we introduce and study class of modules which are proper generalization of both the purely extending modules and G-extending modules.
We call an R-module M is purely Goldie extending if, for each X ≤ M, there is a pure submodule P of M such that X β P.
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.
American Psychological Association (APA)
al-Saidi, Sad Abd al-Kazim& Umar, Iqbal Ahmad. 2015. Purely goldie extending modules. Ibn al-Haitham Journal for Pure and Applied Science،Vol. 28, no. 2, pp.147-154.
https://search.emarefa.net/detail/BIM-618649
Modern Language Association (MLA)
al-Saidi, Sad Abd al-Kazim& Umar, Iqbal Ahmad. Purely goldie extending modules. Ibn al-Haitham Journal for Pure and Applied Science Vol. 28, no. 2 (2015), pp.147-154.
https://search.emarefa.net/detail/BIM-618649
American Medical Association (AMA)
al-Saidi, Sad Abd al-Kazim& Umar, Iqbal Ahmad. Purely goldie extending modules. Ibn al-Haitham Journal for Pure and Applied Science. 2015. Vol. 28, no. 2, pp.147-154.
https://search.emarefa.net/detail/BIM-618649
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 153
Record ID
BIM-618649