Purity and projectivity relative to a submodule
Author
Source
المجلة العراقية للعلوم الإحصائية
Publisher
University of Mosul College of Computer Science and Mathematics
Publication Date
2013-12-31
Country of Publication
Iraq
No. of Pages
14
Main Subjects
English Abstract
In the literature there are some links between the notions of directsummands, purity and projectivity.
In this paper, we study these links among the notions but relative to an arbitrary submodules, also a partial links are consider.
Properties and characterizations of these notions which are correspondence, have been given.Among others, the following have been proved.
If M is a projective module, every pure submoduleN relative to a submodule T is projective relative to N > T.
Also if Mis an R-module with R is M-injective, then every projective submoduleof M relative to T is pure relative to T.
As a consequence of the above.
If M > R is quasi-continuous, then M is injective and every projectivesubmodule relative to T is pure relative to T.
Data Type
Conference Papers
Record ID
BIM-345586
American Psychological Association (APA)
Abbas, Mahdi Sadiq. 2013-12-31. Purity and projectivity relative to a submodule. المؤتمر العلمي لكلية علوم الحاسوب و الرياضيات (6 : 2013 : الموصل، العراق). . Vol. 13, no. 25 (2013), pp.49-62.الموصل، العراق : جامعة الموصل، كلية علوم الحاسبات و الرياضيات،.
https://search.emarefa.net/detail/BIM-345586
Modern Language Association (MLA)
Abbas, Mahdi Sadiq. Purity and projectivity relative to a submodule. . الموصل، العراق : جامعة الموصل، كلية علوم الحاسبات و الرياضيات،. 2013-12-31.
https://search.emarefa.net/detail/BIM-345586
American Medical Association (AMA)
Abbas, Mahdi Sadiq. Purity and projectivity relative to a submodule. . المؤتمر العلمي لكلية علوم الحاسوب و الرياضيات (6 : 2013 : الموصل، العراق).
https://search.emarefa.net/detail/BIM-345586