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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 this paper we dene the monadic Pavelka algebras as algebraic structures induced by the action of quantiers in Rational Pavelka predicate logic. The main result is a representation theorem for these structures.

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)