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

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

2007-07-30

arxiv.org/abs/0707.4449v2

Mathematics

Commutative Algebra

16 pages, in French. Accepted for publication in Algebra and Number Theory. Change of title and minor changes in the text, fol

Scientific paper

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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