Decidability for the theory of modules over a Prüfer domain

Lorna Gregory

doi:10.1093/imrn/rnac318

Decidability for the theory of modules over a Prüfer domain

Lorna Gregory

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

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Abstract

In this article we give elementary conditions completely characterising when the theory of modules of a Prüfer domain is decidable. Using these results, we show that the theory of modules of the ring of integer valued polynomials is decidable.

Original language	English
Pages (from-to)	16574–16673
Number of pages	100
Journal	International Mathematics Research Notices
Volume	2023
Issue number	19
Early online date	28 Dec 2022
DOIs	https://doi.org/10.1093/imrn/rnac318
Publication status	Published - Oct 2023

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title = "Decidability for the theory of modules over a Pr{\"u}fer domain",

abstract = "In this article we give elementary conditions completely characterising when the theory of modules of a Pr{\"u}fer domain is decidable. Using these results, we show that the theory of modules of the ring of integer valued polynomials is decidable.",

author = "Lorna Gregory",

note = "Funding information: This work was supported by PRIN 2017-Mathematical Logic: models, sets, computability prot. 2017NWTM8R_004.",

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AB - In this article we give elementary conditions completely characterising when the theory of modules of a Prüfer domain is decidable. Using these results, we show that the theory of modules of the ring of integer valued polynomials is decidable.

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Decidability for the theory of modules over a Prüfer domain

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