title: The unique maximal GF-regular submodule of a module.
abstract: 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 r(n)tr(n)a = r(n)a. We proved that each unitary R-module A contains a unique maximal GF-regular submodule, which we denoted by M GF(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∩M GF(A). Moreover, if A is projective, then MGF(A) is a G-pure submodule of A and MGF(A) = M(R) · A.
authors.affiliation: Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China.
authors.forename: Areej M
authors.initials: AM
authors.lastname: Abduldaim
authors.forename: Sheng
authors.initials: S
authors.lastname: Chen