Decidability of the theory of modules over prüfer domains with infinite residue fields

Lorna Gregory; Sonia L'Innocente; Gena Puninski; Carlo Toffalori

doi:10.1017/jsl.2018.58

Decidability of the theory of modules over prüfer domains with infinite residue fields

Lorna Gregory, Sonia L'Innocente, Gena Puninski, Carlo Toffalori

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1391-1412
Number of pages	22
Journal	Journal of Symbolic Logic
Volume	83
Issue number	4
DOIs	https://doi.org/10.1017/jsl.2018.58
Publication status	Published - 1 Dec 2018

Keywords

Bézout domain
decidability
prime radical relation
Prüfer domain

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10.1017/jsl.2018.58

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abstract = "We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Pr{\"u}fer (in particular B{\'e}zout) domains with infinite residue fields in terms of a suitable generalization of the prime radical relation. For B{\'e}zout domains these conditions are also necessary.",

keywords = "B{\'e}zout domain, decidability, prime radical relation, Pr{\"u}fer domain",

author = "Lorna Gregory and Sonia L'Innocente and Gena Puninski and Carlo Toffalori",

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AU - Gregory, Lorna

AU - L'Innocente, Sonia

AU - Puninski, Gena

AU - Toffalori, Carlo

N1 - Publisher Copyright: © The Association for Symbolic Logic 2018.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - 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.

AB - 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.

KW - Bézout domain

KW - decidability

KW - prime radical relation

KW - Prüfer domain

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JO - Journal of Symbolic Logic

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Decidability of the theory of modules over prüfer domains with infinite residue fields

Abstract

Keywords

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