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We develop the general theory of RMV-algebras, which are essentially unit intervals in Riesz spaces with strong unit. Since the variety of RMV-algebras is generated by [0, 1], we get an equational characterization of the real product on [0,1] interpreted as scalar multiplication.
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-group. We also provide a categorical framework and we prove the… (More)