  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.
