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.
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Notes
The next Proposition 6.4 implies that the converse is also true.
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Lorna Gregory and Carlo Toffalori thank the Italian GNSAGA-INdAM and PRIN 2017 for their support. The authors thank the anonymous referee for her/his very helpful suggestions.
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Gregory, L., Herzog, I. & Toffalori, C. Notes on model theory of modules over Dedekind domains. Boll Unione Mat Ital 17, 11–39 (2024). https://doi.org/10.1007/s40574-023-00372-w
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DOI: https://doi.org/10.1007/s40574-023-00372-w