Abstract
As is well known, Zadeh (1965) introduced the notion of a fuzzy subset of a nonempty set X as a function from X to unit real interval = [0, 1]. I The notion of fuzzy groups was introduced by Rosenfeld (1971). Many scientists studied in basic properties about fuzzy groups and ideals. In these years Barnes (1966), Booth (1992), Luh (1969) and Coppage (1971) studied about gamma rings. The concept of fuzzy ideal in -ring was introduced by Jun and Lee (1992). They studied some preliminary properties of fuzzy ideals of -rings. In the last years Dutta and Chanda (2005) and Hong and Jun (1995) improved these works. Booth and Groenawald (1992) analised the prime modules of gamma ring. In this paper, we define fuzzy submodule of M Γ module G and give some basic characterization of it. That is if μ is fuzzy submodule of M Γ module G if and only if [ ] 0,1 t ∀ ∈ ,