ON PROJECTIVE L- MODULES

ABSTRACT. The concepts of free modules, projective modules, injective modules and the like form an important area in module theory. The notion of free fuzzy modules was introduced by Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameri introduced the concept of projective and injective L-modules. In this paper we give an alternate definition for projective L-modules. We prove that every free L-module is a projective L-module. Also we prove that if µ∈L(P) is a projective L-module, and if 0 0f gη ν µ → → → → is a short exact sequence of L-modules then η ⊕ µ>ν. Further it is proved that if µ∈L(P) is a projective L-module then µ is a fuzzy direct summand of a free L-module.