Existentially closed models of the theory of Artinian local rings
Hans Schoutens
Abstract
The class of all Artinian local rings of length at most l is A2-elementary, axiomatised by a finite set of axioms Artl. 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 Gorl of all Artinian local Gorenstein rings of length l with algebraically closed residue field is model complete and the theory Artl is companionable, with model-companion Gorl.
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