Behnam Talaee - Department of Mathematics, Faculty of Basic Sciences, Babol Noshirvani University of Technology, Shariati Ave., Babol, Iran Post Code:۴۷۱۴۸-۷۱۱۶۷
Mehrnoosh Sobhani - Department of Mathematics, Faculty of Basic Sciences, Babol Noshirvani University of Technology, Shariati Ave., Babol, Iran Post Code:۴۷۱۴۸-۷۱۱۶۷
Mohammad Javad Nematollahi - Department of Mathematics, Islamic Azad University, Arsanjan Branch, Arsanjan, Iran

In this paper we study about IF binary operations on some IF sets, at first. Then we introduce IF groups, IF modules and IF homo- morphisms under IF binary operations. We present some properties of IF groups rings and modules under binary operation. IF modules and IF homomorphisms over this kind of IF rings are introduced and investigated.

IF operation, IF rings, IF modules, IF homomorphisms