Existentially closed models of the theory of Artinian local rings
Commutative Algebra
2008-02-03 v1 Rings and Algebras
Abstract
The class of all Artinian local rings of length at most l is A_2-elementary, axiomatised by a finite set of axioms Art_l. We show that its existentially closed models are Gorenstein, of length exactly l and their residue fields are algebraically closed, and, conversely, every existentially closed model is of this form. The theory Gor_l of all Artinian local Gorenstein rings of length l with algebraically closed residue field is model complete and the theory Art_l is companionable, with model-companion Gor_l.
Keywords
Cite
@article{arxiv.math/9707231,
title = {Existentially closed models of the theory of Artinian local rings},
author = {Hans Schoutens},
journal= {arXiv preprint arXiv:math/9707231},
year = {2008}
}