MV-modules

In the present paper, we define the MV-modules over PMV-algebras. These are structures that naturally correspond to ℓu-modules over ℓu-rings. Fixing an ℓu-ring (R,υ), we prove the equivalence between the category of ℓu-modules over (R,υ) and the category of MV-modules over Γ(R,υ). We also introduce the truncated modules, that are MV-algebras endowed with an external multiplication defined for any element in the positive cone of an ℓu-ring and we prove the natural equivalence between MV-modules and truncated modules.