Document Type : Research Paper


1 Department of Mathematics, Babol Noshirvani University of Technology, Shariati Ave., Babol, Iran

2 Department of Mathematics, Yazd University, Iran


In this paper, we discuss the structure of intuitionistic fuzzy projec- tive modules and investigate some properties of them. Also we study about intuitionistic fuzzy homomorphisms between intuitionistic fuzzy modules.

We study about exact sequences, products and co-products, func- tors and relating topics in IFR − Mod and investigate the relationship between them, where IFR − Mod is category whose objects are intu- itionidtic fuzzy modules and morphisms are intuitionistic fuzzy homo-


For a commutative ring R and two intuitionistic fuzzy R- modules

A = (μA, νA) ≤IF M, B = (μB, νB) ≤IF N we show that

HomIF −R (A, B) = (α, β) is an intuitionistic fuzzy R-module.

Also for a commutative ring R, if

0⟶𝐴𝑓~→ B 𝑔~→ C is an exact sequence in IFR-Mod, where f˜ is IF split homomorphism, then

we show that HomIF −R(D,-) preserves the sequence, for every D ∈ IFR − Mod.


Main Subjects