The Unique Maximal GF-Regular Submodule of a Module. (15th September 2013)

• Record Type: Journal Article
• Authors: Abduldaim, Areej M.; Chen, Sheng
• Other Names: He J. Academic Editor.; Ivanov I. G. Academic Editor.; Rada J. Academic Editor.; Székelyhidi L. Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2013(2013)
• Publication Date: 2013-09-15
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2013/750808
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : An R -module A is called G F -regular if, for each a ∈ A and r ∈ R, there exist t ∈ R and a positive integer n such that r n t r n a = r n a . We proved that each unitary R -module A contains a unique maximal G F -regular submodule, which we denoted by M G F ( 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 M G F ( K ) = K ∩ M G F ( A ) . Moreover, if A is projective, then M G F ( A ) is a G -pure submodule of A and M G F ( A ) = M ( R ) · A .