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This paper aims at connecting the various classes that provide an algebraicsemantics for three different conservative expansions of Lukasiewicz logic,using algebraic and category-theoretical techniques. We connect such classes ofalgebras by adjunctions, using the tensor product of MV-algebras and definingthe tensor PMV-algebra of a semisimple MV-algebra, inspired by the constructionof the tensor algebra of a vector space. We further apply the main results toprove amalgamation properties and, via categorical equivalence, we transfer allresults to the framework of lattice- ordered groups.

A general view of the algebraic semantics of \L ukasiewicz logic with product