  In this paper we study the tensor product for MV-algebras, the algebraic
structures of \L ukasiewicz $\infty$-valued logic. Our main results are: the
proof that the tensor product is preserved by the categorical equivalence
between the MV-algebras and abelian lattice-order groups with strong unit and
the proof of the scalar extension property for semisimple MV-algebras. We
explore consequences of this results for various classes of MV-algebras and
lattice-ordered groups enriched with a product operation.
