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

Scalar extensions for algebraic structures of Lukasiewicz logic