Semiring and semimodule issues in MV-algebras

Details Semiring and semimodule issues in MV-algebras Semiring and semimodule issues in MV-algebras

2010-02-21

arxiv.org/abs/1002.4013v6

Mathematics

Rings and Algebras

To appear in Communications in Algebra

Scientific paper

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.

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