Putting together Lukasiewicz and product logics

In this paper we investigate a propositional fuzzy logical system L? which contains the well-known Lukasiewicz, Product and Godel fuzzy logics as sublogics. We define the corresponding algebraic structures, called L?-algebras and prove the following completeness result: a formula f is provable in the L? logic iff it is a tautology for all linear L?-algebras. Moreover, linear L?-algebras are shown to be embeddable in linearly ordered abelian rings with a strong unit and cancellation law.