Somayeh Karimzadeh - Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box ۷۷۱۸۸۹۷۱۱۱, Rafsanjan, Iran.
Somayeh Hadjirezaei - Department of Mathematics, Vali-e-Asr University of Rafsanjan, P.O. Box ۷۷۱۸۸۹۷۱۱۱, Rafsanjan, Iran.

 Let R be a commutative ring with identity and M be a finitely generated unital R-module. In this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. Moreover, we investigate some conditions which imply that the module M is the direct sum of some cyclic modules and free modules. Then some properties of Fitting ideals of modules which are the direct sum of finitely generated module and finitely generated multiplication module are shown. Finally, we study some properties of modules that are the direct sum of multiplication modules in terms of Fitting ideals.

Fitting ideals, multiplication module, projective module