MV-algebras with operators (the commutative and the non-commutative case)

In the present paper we define the (pseudo) MV-algebras with <f>n</f>-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 <f>ℓ</f>-group. We also provide a categorical framework and we prove the analogue of Mundici's categorical equivalence between MV-algebras and abelian <f>ℓ</f>-groups with strong unit. Thus, the category of pseudo MV-algebras with operators is equivalent to some category of <f>ℓ</f>-groups with operators. [Copyright &y& Elsevier]