Existentially closed models of the theory of Artinian local rings

Details Existentially closed models of the theory of Artinian local rings Existentially closed models of the theory of Artinian local rings

1997-07-11

arxiv.org/abs/math/9707231v1

Mathematics

Commutative Algebra

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Existentially closed models of the theory of Artinian local rings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Existentially closed models of the theory of Artinian local rings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Existentially closed models of the theory of Artinian local rings will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-446974