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Nonsingular Hasse principle for rings,

by L. Darnière.

Journal für die reine und angewandte Mathematik, 529 (2000), 75-100
Submitted in June 98.

Short abstract
In this paper we introduce a local global principle for rings inspired by Hasse's principle, that we call LGPH. We prove that the class of rings satisfying the LGPH is recursively axiomatisable (in the language of rings). We use this result to give a natural recursive axiomatisation of the ring of p-adic algebraic integers, that is the integral closure of the ring of integers inside the field of p-adic numbers. As a consequence we prove that this ring is decidable.

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

Electronic version of the paper
Version February 99: dvi, Postscript.
Version July 98: dvi, Postscript.
Version March 98: dvi, Postscript.