Algebras of Lukasiewicz's logic and their semiring reducts

In this paper we shall establish some links between the algebras of Lukasiewicz logic (MV-algebras) and the semirings. The relationship of these algebraic structures gives a hint on how to construct linear algebra starting from MV-algebras. Indeed here the role of sum and product is played respectively by a lattice operation and by an arithmetical operation. In this way, following the tradition of semirings, it makes full sense to consider "many-valued automata" and "many-valued formal languages" interpreted in Lukasiewicz logic.