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DECIDABILITY OF THE THEORY OF MODULES OVER PRÜFER DOMAINS WITH INFINITE RESIDUE FIELDS

Published online by Cambridge University Press:  21 December 2018

LORNA GREGORY ,
SONIA L’INNOCENTE ,
GENA PUNINSKI  and
CARLO TOFFALORI
LORNA GREGORY
Affiliation:
SCHOOL OF SCIENCE AND TECHNOLOGIES DIVISION OF MATHEMATICS UNIVERSITY OF CAMERINO VIA MADONNA DELLE CARCERI 9 CAMERINO 62032, ITALYE-mail: lorna.gregory@gmail.com
SONIA L’INNOCENTE
Affiliation:
SCHOOL OF SCIENCE AND TECHNOLOGIES DIVISION OF MATHEMATICS UNIVERSITY OF CAMERINO VIA MADONNA DELLE CARCERI 9 CAMERINO 62032, ITALYE-mail: sonia.linnocente@unicam.it
GENA PUNINSKI
Affiliation:
FACULTY OF MECHANICS AND MATHEMATICS BELARUSIAN STATE UNIVERSITY AV. NEZALEZHNOSTI 4 MINSK 220030, BELARUS
CARLO TOFFALORI
Affiliation:
SCHOOL OF SCIENCE AND TECHNOLOGIES DIVISION OF MATHEMATICS UNIVERSITY OF CAMERINO VIA MADONNA DELLE CARCERI 9 CAMERINO 62032, ITALYE-mail: carlo.toffalori@unicam.it
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Abstract

We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Prüfer (in particular Bézout) domains with infinite residue fields in terms of a suitable generalization of the prime radical relation. For Bézout domains these conditions are also necessary.

Keywords

Primary 03C6003C9803B2513F05Prüfer domainBézout domainprime radical relationdecidability
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 4 , December 2018 , pp. 1391 - 1412
Copyright
Copyright © The Association for Symbolic Logic 2018 

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References

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