B\'ezout domains and lattice-valued modules
Logic
2018-06-08 v4
Abstract
Let B be a commutative B\'ezout domain B and let MSpec(B) be the maximal spectrum of B. We obtain a Feferman-Vaught type theorem for the class of B-modules. We analyse the definable sets in terms, on one hand, of the definable sets in the classes of modules over the localizations of B by the maximal ideals of B, and on the other hand, of the constructible subsets of MSpec(B). When B has good factorization, it allows us to derive decidability results for the class B-modules, in particular when B is the ring of algebraic integers or its intersection with real numbers or p-adic numbers.
Cite
@article{arxiv.1604.05922,
title = {B\'ezout domains and lattice-valued modules},
author = {Sonia L'Innocente and Françoise Point},
journal= {arXiv preprint arXiv:1604.05922},
year = {2018}
}
Comments
This improves a previous version put on ArXiv, following the same strategy but proving an intermediate result (Theorem 3.2) in a more adequate way