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In the present paper we define the (pseudo) MV-algebras with n-ary operators, generalizing MV-modules and product MV-algebras. Our main results assert that there are bijective correspondences between the operators defined on a pseudo MV-algebra and the operators defined on the corresponding ℓ-group. We also provide a categorical framework and we prove the analogue of Mundici's categorical equivalence between MV-algebras and abelian ℓ-groups with strong unit. Thus, the category of pseudo MV-algebras with operators is equivalent to some category of ℓ-groups with operators. [Copyright &y& Elsevier]

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. [Copyright &y& Elsevier]