MV-algebras of continuous functions and l-monoids

Abstract

A. Di Nola & S.Sessa [8] showed that two compact spaces X and Y are homeomorphic if the MV-algebras C(X,I) and C(Y,I) of continuous functions defined on X and Y respectively are isomorphic. And they proved that A is a semisimple MV-algebra iff A is a subalgebra of C(X) for some compact Hausdorff space X. In this paper, firstly by use of functorial argument, we show these characterization theorems. Furthermore we obtain some other functorial results between topological spaces and MV-algebras. Secondly as a classical problem, we find a necessary and sufficient condition on a given residuated l-monoid that it is segmenently embedded into an l-group with order unit.