Some properties of Intuitionistic fuzzy modules

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-morphisms.For a commutative ring R and two intuitionistic fuzzy R- modulesA = (μA, νA) ≤IF M, B = (μB, νB) ≤IF N we show thatHomIF −R (A, B) = (α, β) is an intuitionistic fuzzy R-module.Also for a commutative ring R, if۰⟶𝐴𝑓~→ B 𝑔~→ C is an exact sequence in IFR-Mod, where f˜ is IF split homomorphism, thenwe show that HomIF −R(D,-) preserves the sequence, for every D ∈ IFR − Mod.

کلیدواژه ها:

IF projective modules ، IF exact sequences ، IF hom functors