Purity and projectivity relative to a submodule

Author

Abbas, Mahdi Sadiq

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

Mathematics

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

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