A generalization of von Neumann regularity

Annals of Pure and Applied Logic 135 (1-3):210-242 (2005)
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Abstract

We propose two theories, one generalizing the notion of regularity, the other symmetric to it. Under two additional axioms one obtains model completeness of both theories. Models of these theories can be viewed as rings of sections of sheaves whose stalks are valuation rings. Regular rings correspond to the special case where all stalks are trivial valuation rings, that is fields

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10.1016/j.apal.2005.02.002

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Citations of this work

A valuation ring analogue of von Neumann regularity.Claude Sureson - 2007 - Annals of Pure and Applied Logic 145 (2):204-222.
Model companion and model completion of theories of rings.Claude Sureson - 2009 - Archive for Mathematical Logic 48 (5):403-420.

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References found in this work

Model Theoretic Algebra. Selected Topics.Greg Cherlin - 1982 - Journal of Symbolic Logic 47 (1):222-223.

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