Existentially closed models of the theory of Artinian local rings

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dc.creatorSchoutens, Hans
dc.date1997-07-11
dc.date.accessioned2026-07-07T09:15:48Z
dc.date.available2026-07-07T09:15:48Z
dc.descriptionThe 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.
dc.identifierhttps://arxiv.org/abs/math/9707231
dc.identifierhttp://arxiv.org/abs/math/9707231
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/153140
dc.subjectCommutative Algebra
dc.subjectRings and Algebras
dc.titleExistentially closed models of the theory of Artinian local rings
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