Gamma Modules R. Ameri, R. Sadeghi Department of Mathematics, Faculty of Basic Science University of Mazandaran, Babolsar, Iran e-mail: ameri@umz.ac.ir Abstract Let R be a Γ-ring. We introduce the notion of gamma modules over R and study important properties of such modules. In this regards we study submodules and homomorphism of gamma modules and give related basic results of gamma modules. Keywords: Γ-ring, R Γ -module, Submodule, Homomorphism. 1 Introduction The notion of a Γ-ring was introduced by N. Nobusawa in [6]. Recently, W.E. Barnes [2], J. Luh [5], W.E. Coppage studied the structure of Γ-rings and obtained various gen- eralization analogous of corresponding parts in ring theory. In this paper we extend the concepts of module from the category of rings to the category of R Γ -modules over Γ-rings. Indeed we show that the notion of a gamma module is a generalization of a Γ-ring as well as a module over a ring, in fact we show that many, but not all, of the results in the Ratio Mathematica 20, 2010 127