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arXiv · 0707.4449

Sur la définissabilité existentielle de la non-nullité dans les anneaux

Laurent Moret-Bailly
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Abstract

We investigate the rings in which the set of nonzero elements is positive-existential (i.e. a finite union of projections of "algebraic" sets). In the case of Noetherian domains, we prove in particular that this condition is satisfied whenever the ring in question is not local Henselian, while it is not satisfied for any excellent local Henselian domain which is not a field. As a byproduct, we obtain an answer to a question of Popescu on strong approximation for Henselian pairs.

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BibTeXRIS

Laurent Moret-Bailly. 2007-10-19. Sur la définissabilité existentielle de la non-nullité dans les anneaux. https://arxiv.org/abs/0707.4449

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