MVW-rigs

Abstract

In this paper, a new algebraic structure is defined, which is a new MV-algebra that has a product operation, we will call it MVW-rig (Multivalued-weak rig). This structure is defined with universal algebra axioms, it is presented with a good amount of natural examples in the MV-algebra environment and the first results having to do with ideal, quotients, homomorphisms and subdirect product are established. In particular, its prime spectrum is studied, that with the co-Zariski topology it is compact. Consequently, a good number of results that are analogous to the theory of commutative rings and rigs are presented with which this theory keeps a close relationship to.