Bezout domains and lattice-valued modules

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

L'Innocente, Sonia¹  Point, Frangoise^2,3 

[1] Univ Camerino, Sch Sci & Technol, Dept Math, Via Madonna Carceri 9, I-62032 Camerino, MC, Italy

[2] Univ Mons, Dept Math De Vinci, 20 Pl Parc, B-7000 Mons, Belgium

[3] Fonds Rech Sci FNRS FRS, Brussels, Belgium

关键词: Bezout domains;    Decidability of theories of modules;    Valued modules;    Abelian structures;   

DOI  :  10.1016/j.jpaa.2019.05.016

来源: Elsevier

【 摘 要 】

Let B be a commutative Bezout domain and let MSpec(B) be the maximal spectrum of B. We obtain a Feferman-Vaught type theorem for the class Mod-B of all (right) B-modules. We analyze the definable sets in terms, on the one hand, of the definable sets in the classes Mod-B-M, where B-M ranges over the localizations of B at M, M is an element of MSpec(B), and on the other hand, of the constructible subsets of MSpec(B). This allows us to derive decidability results for the class Mod-B, in particular when B is the ring (Z) over tilde of algebraic integers or one of the rings (Z) over tilde boolean AND R, (Z) over tilde boolean AND Q(p). (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free