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Preprint Number 1192

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1192. Eudes Naziazeno, Marco Barone, Nicolás Caro
First-order definability of rational integers in a class of polynomial rings (first version)

Submission date: 24 March 2017


In this paper, we prove first-order definability of the ground ring of integers, inside a polynomial ring with coefficients in a reduced indecomposable (commutative, unital) ring, provided the definability of a suitable subset of the constants. This extends a result, that has long been known to hold for integral domains (Robinson, 1952, Denef 1978) to a wider class of coefficient rings. We also provide an example of such a coefficient ring, which is not a domain, for which the requirement of having a definable subset is actually met.

Mathematics Subject Classification:

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Full text: arXiv 1703.08266: pdf, ps.

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