The construction of fractions of \Gamma-module over commutative \Gamma-ring

The aim of this paper is to construct fraction of \Gamma-module over commutative \Gamma-ring. There should be an appropriate set S of elements in a \Gamma-ring R to be used as \Gamma-module of fractions. Then we study the homomorphisms of \Gamma-module which can lead to related basic results. We show that for every \Gamma-module M, S^{-۱}(۰:_R M)=(۰:_{S^{-۱}R} S^{-۱}M). Also, if M is a finitely generated R_\Gamma-module, then S^{-۱}M is finitely generated.