Pseudo algebraically closed rings,

by L. Darnière.

Manuscripta Mathematica, 105 (2001), no. 1, 13-46

Submitted on March 99.

Short abstract

We use a variant of the nonsingular Hasse Principle to define a class of rings analogeous to PAC fields, and prove that this class has nice model theoretical properties. Since there are a lot of examples of such rings which are of interest for arithmetical purpose we apply our study to those examples, obtaining several decidability results and one purely algebraic application.

Mathematics Subject Classification

12L05 Decidability related to field theory
03B25 Decidability of theories and sets of sentences

Electronic version of the paper

Version August 99 (37 pages): dvi, Postscript.
Version March 99 (27 pages, obsolete): dvi, Postscript.