On complete and strongly stonian MV-algebras

We solve positively a conjecture of L. P. Belluce by using the notion of singular element of an $MV$-algebra. This concept implies a decomposition theorem for complete $MV$-algebras, formally analogous to that one for lattice-ordered complete groups. We also prove that strongly stonian $MV$-algebras correspond, via the well known functor $\Gamma$, to lattice-ordered Abelian groups with strong unit which are strongly projectable. We solve positively a conjecture of L. P. Belluce by using the notion of singular element of an $MV$-algebra. This concept implies a decomposition theorem for complete $MV$-algebras, formally analogous to that one for lattice-ordered complete groups. We also prove that strongly stonian $MV$-algebras correspond, via the well known functor $\Gamma$, to lattice-ordered Abelian groups with strong unit which are strongly projectable. We solve positively a conjecture of L. P. Belluce by using the notion of singular element of an $MV$-algebra. This concept implies a decomposition theorem for complete $MV$-algebras, formally analogous to that one for lattice-ordered complete groups. We also prove that strongly stonian $MV$-algebras correspond, via the well known functor $\Gamma$, to lattice-ordered Abelian groups with strong unit which are strongly projectable.