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DECIDABILITY OF MODULES OVER A BÉZOUT DOMAIN D+XQ[X] WITH D A PRINCIPAL IDEAL DOMAIN AND Q ITS FIELD OF FRACTIONS

Published online by Cambridge University Press:  17 April 2014

GENA PUNINSKI  and
CARLO TOFFALORI
GENA PUNINSKI
Affiliation:
DEPARTMENT OF MATHEMATICS, BELARUSIAN STATE UNIVERSITY, PRASPEKT NEZALEZHNOSTI 4, MINSK 220030, BELARUSE-mail:[email protected]
CARLO TOFFALORI
Affiliation:
UNIVERSITY OF CAMERINO, SCHOOL OF SCIENCE AND TECHNOLOGIES, DIVISION OF MATHEMATICS, VIA MADONNA DELLE CARCERI 9, 62032 CAMERINO, ITALYE-mail:[email protected]
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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.

Keywords

03C6013F0513F30Bézout domaindecidabilityZiegler spectrumCantor–Bendixson rankKrull–Gabriel dimension
Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 1 , March 2014 , pp. 296 - 305
Copyright
Copyright © Association for Symbolic Logic 2014 

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References

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