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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Michael F. Singer
Journal: Proc. Amer. Math. Soc. 135 (2007), 1929-1934
MSC (2000): Primary 03C10; Secondary 35A05, 12H05
Published electronically: January 12, 2007
MathSciNet review: 2286106
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Abstract: 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.


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Additional Information

Michael F. Singer
Affiliation: Department of Mathematics, North Carolina State University, Box 8205, Raleigh, North Carolina 27695-8205
Email: singer@math.ncsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08653-4
PII: S 0002-9939(07)08653-4
Received by editor(s): November 25, 2005
Received by editor(s) in revised form: January 21, 2006
Published electronically: January 12, 2007
Additional Notes: The preparation of this article was partially supported by NSF Grant CCR-0096842.
Communicated by: Julia Knight
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.