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Creators/Authors contains: "Naziazeno, Eudes"

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  1. ; ; ; (, International Mathematics Research Notices)
    null (Ed.)
    Abstract We characterize those finitely generated commutative rings which are (parametrically) bi-interpretable with arithmetic: a finitely generated commutative ring A is bi-interpretable with $$(\mathbb{N},{+},{\times })$$ 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 $$\mathbb{Z}$$. Notably, by constructing a nontrivial derivation on a nonstandard model of arithmetic we show that the ring of dual numbers over $$\mathbb{Z}$$ is not bi-interpretable with $$\mathbb{N}$$. 
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