A valuation ring analogue of von Neumann regularity

Annals of Pure and Applied Logic 145 (2):204-222 (2007)
  Copy   BIBTEX

Abstract

We continue the study of a theory which is a valued analogue of the theory of regular rings studied by Carson, Lipshitz and Saracino, characterize it as the model companion of the theory of Prüfer rings, and prove its decidability. We then link it to the theory of p.p. rings developed by Weispfenning and show that it admits quantifier elimination in a related language

Categories

Keywords

Reprint years

DOI

10.1016/j.apal.2006.07.001

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 93,296

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Model companion and model completion of theories of rings.Claude Sureson - 2009 - Archive for Mathematical Logic 48 (5):403-420.
A generalization of von Neumann regularity.Claude Sureson - 2005 - Annals of Pure and Applied Logic 135 (1-3):210-242.
Towards the decidability of the theory of modules over finite commutative rings.Gena Puninski & Carlo Toffalori - 2009 - Annals of Pure and Applied Logic 159 (1-2):49-70.
Commutative regular rings and Boolean-valued fields.Kay Smith - 1984 - Journal of Symbolic Logic 49 (1):281-297.
Boolean products of real closed valuation rings and fields.Jorge I. Guier - 2001 - Annals of Pure and Applied Logic 112 (2-3):119-150.
Corps portant un nombre fini de valuations.Françoise Delon - 1987 - Journal of Symbolic Logic 52 (4):994-1004.
Uniformly defining valuation rings in Henselian valued fields with finite or pseudo-finite residue fields.Raf Cluckers, Jamshid Derakhshan, Eva Leenknegt & Angus Macintyre - 2013 - Annals of Pure and Applied Logic 164 (12):1236-1246.
Elementary equivalence of some rings of definable functions.Vincent Astier - 2008 - Archive for Mathematical Logic 47 (4):327-340.
Review: G. L. Cherlin, The Model-Companion of a Class of Structures; L. Lipshitz, D. Saracino, The Model Companion of the Theory of Commutative Rings Without Nilpotent Elements; Angus Macintyre, Model-Completeness for Sheaves of Structures. [REVIEW]Stephen D. Comer - 1983 - Journal of Symbolic Logic 48 (2):496-496.
Weakly minimal modules over integral group rings and over related classes of rings.Stefano Leonesi, Sonia L'Innocente & Carlo Toffalori - 2005 - Mathematical Logic Quarterly 51 (6):613-625.

Analytics

Added to PP
2013-12-30

Downloads
2 (#1,819,493)

6 months
10 (#308,815)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Model companion and model completion of theories of rings.Claude Sureson - 2009 - Archive for Mathematical Logic 48 (5):403-420.

Add more citations

References found in this work

A generalization of von Neumann regularity.Claude Sureson - 2005 - Annals of Pure and Applied Logic 135 (1-3):210-242.

Add more references