On injective L-modules

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 injective L-modules and prove that a direct sum of L-modules is injective if and only if each L-module in the sum is injective. Also we prove that if J is an injective module and μ is an injective L-submodule of J , and if 0 → μ f −→ ν g −→ η → 0 is a short exact sequence of L-modules, then ν μ⊕η.