Model theory of partial differential fields: From commuting to noncommuting derivations

McGrail (2000) has shown the existence of a model completion for the universal theory of fields on which a finite number of commuting derivations act and, independently, Yaffe (2001) has shown the existence of a model completion for the univeral theory of fields on which a fixed Lie algebra acts as...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2007-06, Vol.135 (6), p.1929-1934
Main Author: Singer, Michael F.
Format: Article
Language:English
Subjects:
Algebra
Axioms
Commuting
Differentials
Exact sciences and technology
General mathematics
General, history and biography
Logic and foundations
Logical proofs
Mathematical logic, foundations, set theory
Mathematical rings
Mathematical theorems
Mathematics
Model theory
Nonassociative rings and algebras
Number theory
Polynomials
Sciences and techniques of general use
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Summary:McGrail (2000) has shown the existence of a model completion for the universal theory of fields on which a finite number of commuting derivations act and, independently, Yaffe (2001) has shown the existence of a model completion for the univeral theory of fields on which a fixed Lie algebra acts as derivations. We show how to derive the second result from the first.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-07-08653-4