Publications > Preprint server > Preprint Number 1114
Preprint Number 1114
1114. Matthias Aschenbrenner, Anatole Khélif, Eudes Naziazeno, Thomas Scanlon The logical complexity of finitely generated commutative rings E-mail: Submission date: 15 October 2016 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 (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. Mathematics Subject Classification: Keywords and phrases: |
Last updated: March 23 2021 09:20 | Please send your corrections to: |