Decidability of the theory of modules over Prüfer domains with dense value groups

Lorna Gregory; Sonia L'Innocente; Carlo Toffalori

doi:10.1016/j.apal.2019.102719

Decidability of the theory of modules over Prüfer domains with dense value groups

Lorna Gregory, Sonia L'Innocente, Carlo Toffalori

Algebra, Number Theory, Logic, and Representations (ANTLR)

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

1 Citation (Scopus)

Abstract

We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Prüfer (in particular Bézout) domains whose localizations at maximal ideals have dense value groups. For Bézout domains, these conditions are also necessary.

Original language	English
Article number	102719
Journal	Annals of Pure and Applied Logic
Volume	170
Issue number	12
DOIs	https://doi.org/10.1016/j.apal.2019.102719
Publication status	Published - Dec 2019

Keywords

Bézout domain
Decidability
Dense value group
Prüfer domain

Access to Document

10.1016/j.apal.2019.102719

Cite this

@article{b7f7299ec5744066a8062a7de1373f26,

title = "Decidability of the theory of modules over Pr{\"u}fer domains with dense value groups",

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 whose localizations at maximal ideals have dense value groups. For B{\'e}zout domains, these conditions are also necessary.",

keywords = "B{\'e}zout domain, Decidability, Dense value group, Pr{\"u}fer domain",

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

note = "Funding Information: The second and third authors thank the Italian GNSAGA-INdAM for its support. Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",

year = "2019",

month = dec,

doi = "10.1016/j.apal.2019.102719",

language = "English",

volume = "170",

journal = "Annals of Pure and Applied Logic",

issn = "0168-0072",

publisher = "Elsevier",

number = "12",

}

TY - JOUR

T1 - Decidability of the theory of modules over Prüfer domains with dense value groups

AU - Gregory, Lorna

AU - L'Innocente, Sonia

AU - Toffalori, Carlo

PY - 2019/12

Y1 - 2019/12

N2 - We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Prüfer (in particular Bézout) domains whose localizations at maximal ideals have dense value groups. 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 whose localizations at maximal ideals have dense value groups. For Bézout domains, these conditions are also necessary.

KW - Bézout domain

KW - Decidability

KW - Dense value group

KW - Prüfer domain

UR - http://www.scopus.com/inward/record.url?scp=85069741064&partnerID=8YFLogxK

U2 - 10.1016/j.apal.2019.102719

DO - 10.1016/j.apal.2019.102719

M3 - Article

AN - SCOPUS:85069741064

VL - 170

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

SN - 0168-0072

IS - 12

M1 - 102719

ER -

Decidability of the theory of modules over Prüfer domains with dense value groups

Abstract

Keywords

Access to Document

Other files and links

Cite this