Decidability of the theory of modules over commutative valuation domains

Gennady Puninskiy; G. Puninski; V. Puninskaya; C. Toffalori

doi:10.1016/j.apal.2006.09.002

Decidability of the theory of modules over commutative valuation domains

Gennady Puninskiy, G. Puninski, V. Puninskaya, C. Toffalori

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

Abstract

We prove that, if V is an effectively given commutative valuation domain such that its value group is dense and archimedean, then the theory of all V-modules is decidable. © 2006 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	258-275
Number of pages	17
Journal	Annals of Pure and Applied Logic
Volume	145
Issue number	3
DOIs	https://doi.org/10.1016/j.apal.2006.09.002
Publication status	Published - Mar 2007

Keywords

Commutative valuation domain
Decidability
Theory of modules
Ziegler spectrum

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10.1016/j.apal.2006.09.002

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title = "Decidability of the theory of modules over commutative valuation domains",

abstract = "We prove that, if V is an effectively given commutative valuation domain such that its value group is dense and archimedean, then the theory of all V-modules is decidable. {\textcopyright} 2006 Elsevier B.V. All rights reserved.",

keywords = "Commutative valuation domain, Decidability, Theory of modules, Ziegler spectrum",

author = "Gennady Puninskiy and G. Puninski and V. Puninskaya and C. Toffalori",

year = "2007",

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doi = "10.1016/j.apal.2006.09.002",

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TY - JOUR

T1 - Decidability of the theory of modules over commutative valuation domains

AU - Puninskiy, Gennady

AU - Puninski, G.

AU - Puninskaya, V.

AU - Toffalori, C.

PY - 2007/3

Y1 - 2007/3

N2 - We prove that, if V is an effectively given commutative valuation domain such that its value group is dense and archimedean, then the theory of all V-modules is decidable. © 2006 Elsevier B.V. All rights reserved.

AB - We prove that, if V is an effectively given commutative valuation domain such that its value group is dense and archimedean, then the theory of all V-modules is decidable. © 2006 Elsevier B.V. All rights reserved.

KW - Commutative valuation domain

KW - Decidability

KW - Theory of modules

KW - Ziegler spectrum

U2 - 10.1016/j.apal.2006.09.002

DO - 10.1016/j.apal.2006.09.002

M3 - Article

SN - 0168-0072

VL - 145

SP - 258

EP - 275

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

IS - 3

ER -

Decidability of the theory of modules over commutative valuation domains

Abstract

Keywords

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