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Preprint Number 1034

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1034. Sonia L'Innocente and Françoise Point
Bézout domains and lattice-valued modules

Submission date: 20 April 2016


We introduce a notion of lattice-valued modules over a commutative Bézout domain B, an instance being the ring B endowed with the lattice-valuation map to its lattice-ordered group of divisibility. Restricting ourselves to the setting of abelian structures satisfying a divisibility condition, we prove a quantifier elimination result. We extend in this setting a former Feferman-Vaught type theorem due to Garavaglia, considering the localizations over the ring B localized at the maximal ideal M, where M ranges over the maximal spectrum of B. We derive decidability results for the theory of modules over certain effectively given Bézout domains with good factorisation and in particular for effectively given good Rumely domains, for example the ring of algebraic integers.

Mathematics Subject Classification: 03C60, 03B25, 13A18, 06F15

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Full text arXiv 1604.05922: pdf, ps.

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