Semiring and semimodule issues in MV-algebras

In this paper we propose a semiring-theoretic approach to MV-algebras based on the connection between such algebras and idempotent semirings - such an approach naturally imposing the introduction and study of a suitable corresponding class of semimodules, called MV-semimodules. We present several results addressed toward a semiring theory for MV-algebras. In particular we show a representation of MV-algebras as a subsemiring of the endomorphism semiring of a semilattice, the construction of the Grothendieck group of a semiring and its functorial nature, and the effect of Mundici categorical equivalence between MV-algebras and lattice-ordered Abelian groups with a distinguished strong order unit upon the relationship between MV-semimodules and semimodules over idempotent semifields.Comment: This version contains some corrections to some results at the end of Section

Álgebras-MV artinianas y noetherianas

We study MV-algebras that satisfacy tha ascending of descending chain conditions on ideals.  We demostrarted, for example, if an MV-algebra is artianan, then it has a finite number of minimal prime ideals. We also show the set of impoicative ideals of an MV-algebra satisfies bothchain conditions provided the algebra, modulo its radical is noetherian. Other results relate tha chain conditions to semi-locality.Estudiamos álgebra-MV que satisfacen las condiciones de cadena ascendente o de cadena descendente por ideales. Por ejemplo, si un álgebra-MV es artiana, enconces tiene un número finito de ideales primos y minimales. También demostramos que el conjunto de ideales implicativos de un álgebra-MV satisface ambas condiciones de cadena si esta álgebra, módulo su radical, es noetheriana. Otris resultados relacionan las condiciones de cadena con la propiedad de ser semi-local

The stable topology for MV-algebras

Like happens in the commutative rings with unit and in the bounded distributive lattices, the pure ideals of A are characterized via the closed subsets of the hull-kernel topology of Max A, the space of the maximal ideals of A. Opens and stable opens of Max A coincide. Some classes of MV-algebras are also described in terms of their pure ideals

Boolean dominated MV-algebras

In this paper the authors study an obvious generalization of the hyperarchimedian MV-algebras: boolean dominated MV-algebras. Particularly they point out the wide difference between the class of the hyperarchimedian MV-algebras and the class of the Boolean dominated MV-algebras