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Preprint Number 640

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640. Gena Puninski and Carlo Toffalori
Decidability of modules over a Bézout domain D + XQ[X] with D a principal ideal domain and Q its field of fractions
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Submission date: 23 October 2013.

Abstract:

We describe the Ziegler spectrum of a Bézout domain B = D + XQ[X] where D is a principal ideal domain and Q is its field of fractions; in particular we compute the Cantor - Bendixson rank of this space. Using this, we prove the decidability of the theory of B-modules when D is “sufficiently” recursive.

Mathematics Subject Classification: 03C60, 13F05, 13F30

Keywords and phrases: Bézout domain, decidability, Ziegler spectrum, Cantor - Bendixson rank, Krull - Gabriel dimension.

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