Bézout域与格值模
Bézout domains and lattice-valued modules
摘要：
设B是交换Bézout整环B，MSpec（B）是B的极大谱.我们得到了B-模类的一个Feferman-Vaught型定理。我们一方面用B的极大理想局部化的模类中的可定义集，另一方面用MSpec（B）的可构造子集来分析可定义集。当B有好的因子分解时，它允许我们导出类B-模的可判定性结果，特别是当B是代数整数代数整数环或它与实数或p-adic数的交集时。
英文摘要：
Let B be a commutative Bézout 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.
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