On the Convergence with Fixed Regulator in Residuated Structures

摘要

The convergence with a fixed regulator has been studied for lattice ordered groups and MV-algebras. In this paper we present some particular results for the case of perfect MV-algebras using Di Nola-Lettieri functors and we extend the notion of convergence with a fixed regulator for residuated lattices. The main results consist of proving that any locally Archimedean MV-algebra has a unique v-Cauchy completion and that in an Archimedean residuated lattice the v-limit is unique.