2019/02/13 by Leloup, Gérard
#Commutative Algebra (math.AC) #FOS: Mathematics #Logic (math.LO) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1902.04839
We prove that there exists a functorial correspondence between MV-algebras and partially cyclically ordered groups which are wound round of lattice-ordered groups. It follows that some results about cyclically ordered groups can be stated in terms of MV-algebras. For example, the study of groups together with a cyclic order allows to get a first-order characterization of groups of unimodular complex numbers and of finite cyclic groups. We deduce a characterization of pseudofinite MV-chains and of pseudo-simple MV-chains (i.e. which share the same first-order properties as some simple ones). We can generalize these results to some non-lineraly ordered MV-algebras, for example hyper-archimedean MV-algebras.