Notes on model theory of modules over Dedekind domains

Lorna Gregory; Ivo Herzog; Carlo Toffalori

doi:10.1007/s40574-023-00372-w

Notes on model theory of modules over Dedekind domains

Lorna Gregory
, Ivo Herzog
, Carlo Toffalori

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

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

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Abstract

We associate a formal power series to every pp-formula over a Dedekind domain and use it to study Ziegler spectra of Dedekind domains $R$ and $\widetilde{R},$ where $R$ a subring of $\widetilde{R}$, with particular interest in the case when $\widetilde{R}$ is the integral closure of $R$ in a finite dimensional separable field extension of the field of fractions of $R$.

Original language	English
Pages (from-to)	11–39
Number of pages	29
Journal	Bollettino dell’Unione Matematica Italiana
Volume	17
Early online date	3 Jul 2023
DOIs	https://doi.org/10.1007/s40574-023-00372-w
Publication status	Published - Mar 2024

Keywords

Dedekind Domain
locally bounded pp-formula
Poincare series
Dedekind domain
Poincaré series
Locally bounded pp-formula
03C60

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abstract = "We associate a formal power series to every pp-formula over a Dedekind domain and use it to study Ziegler spectra of Dedekind domains \$R\$ and \$\textbackslash{}widetilde\{R\},\$ where \$R\$ a subring of \$\textbackslash{}widetilde\{R\}\$, with particular interest in the case when \$\textbackslash{}widetilde\{R\}\$ is the integral closure of \$R\$ in a finite dimensional separable field extension of the field of fractions of \$R\$.",

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AU - Herzog, Ivo

AU - Toffalori, Carlo

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AB - We associate a formal power series to every pp-formula over a Dedekind domain and use it to study Ziegler spectra of Dedekind domains $R$ and $\widetilde{R},$ where $R$ a subring of $\widetilde{R}$, with particular interest in the case when $\widetilde{R}$ is the integral closure of $R$ in a finite dimensional separable field extension of the field of fractions of $R$.

KW - Dedekind Domain

KW - locally bounded pp-formula

KW - Poincare series

KW - Dedekind domain

KW - Poincaré series

KW - Locally bounded pp-formula

KW - 03C60

UR - https://www.scopus.com/pages/publications/85163816249

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DO - 10.1007/s40574-023-00372-w

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SP - 11

EP - 39

JO - Bollettino dell’Unione Matematica Italiana

JF - Bollettino dell’Unione Matematica Italiana

ER -

Notes on model theory of modules over Dedekind domains

Abstract

Keywords

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