The Unique Maximal GF-Regular Submodule of a Module
Joint Authors
Abduldaim, Areej M.
Chen, Sheng
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-3, 3 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-09-15
Country of Publication
Egypt
No. of Pages
3
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
An R-module A is called GF-regular if, for each a∈A and r∈R, there exist t∈R and a positive integer n such that rntrna=rna.
We proved that each unitary R-module A contains a unique maximal GF-regular submodule, which we denoted by MGF(A).
Furthermore, the radical properties of A are investigated; we proved that if A is an R-module and K is a submodule of A, then MGF(K)=K∩MGF(A).
Moreover, if A is projective, then MGF(A) is a G-pure submodule of A and MGF(A)=M(R)·A.
American Psychological Association (APA)
Abduldaim, Areej M.& Chen, Sheng. 2013. The Unique Maximal GF-Regular Submodule of a Module. The Scientific World Journal،Vol. 2013, no. 2013, pp.1-3.
https://search.emarefa.net/detail/BIM-1033267
Modern Language Association (MLA)
Abduldaim, Areej M.& Chen, Sheng. The Unique Maximal GF-Regular Submodule of a Module. The Scientific World Journal No. 2013 (2013), pp.1-3.
https://search.emarefa.net/detail/BIM-1033267
American Medical Association (AMA)
Abduldaim, Areej M.& Chen, Sheng. The Unique Maximal GF-Regular Submodule of a Module. The Scientific World Journal. 2013. Vol. 2013, no. 2013, pp.1-3.
https://search.emarefa.net/detail/BIM-1033267
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1033267