Semiring and semimodule issues in MV-algebras

by A. Di Nola, C. Russo

In this paper we propose a new perspective on the theory of MV-algebras based on the connection between such algebras and idempotent semirings. Such a viewpoint yields, among other results, interesting representation theorems.

We also present some results of more general interest, such as a matrix-based characterization of finitely generated projective semimodules over any semiring and, consequently, the functorial character of the construction of the Grothendieck group of a semiring.