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Preprint Number 1114

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1114. Matthias Aschenbrenner, Anatole Khélif, Eudes Naziazeno, Thomas Scanlon
The logical complexity of finitely generated commutative rings

Submission date: 15 October 2016


We characterize those finitely generated commutative rings which are (parametrically) bi-interpretable with arithmetic: a finitely generated commutative ring A is bi-interpretable with (N, + , × ) if and only if the space of non-maximal prime ideals of A is nonempty and connected in the Zariski topology and the nilradical of A has a nontrivial annihilator in Z. Notably, by constructing a nontrivial derivation on a nonstandard model of arithmetic we show that the ring of dual numbers over Z is not bi-interpretable with N.

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Full text arXiv 1610.04768: pdf, ps.

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