Existentially closed models of the theory of artinian local rings
Copyright policy )Existentially closed models of the theory of artinian local rings
AbstractThe class of all Artinian local rings of length at most l is ∀2-elementary, axiomatised by a finite set of axioms τtl. 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 oτl of all Artinian local Gorenstein rings of length l with algebraically closed residue field is model complete and the theory τtl is companionable, with model-companion oτl.
- University of Toronto Canada
- Wesleyan University United States
- Fields Institute for Research in Mathematical Sciences Canada
Rings and Algebras (math.RA), Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), FOS: Mathematics, Model-theoretic algebra, Commutative Artinian rings and modules, finite-dimensional algebras, Mathematics - Rings and Algebras, Applications of logic to commutative algebra, Mathematics - Commutative Algebra, Commutative Algebra (math.AC)
Rings and Algebras (math.RA), Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), FOS: Mathematics, Model-theoretic algebra, Commutative Artinian rings and modules, finite-dimensional algebras, Mathematics - Rings and Algebras, Applications of logic to commutative algebra, Mathematics - Commutative Algebra, Commutative Algebra (math.AC)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).11 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!