Simple derivations of differentiably simple Noetherian commutative rings in prime characteristic
Author:
V. V. Bavula
Journal:
Trans. Amer. Math. Soc. 360 (2008), 40074027
MSC (2000):
Primary 13N15, 13A35, 16W25
Published electronically:
March 20, 2008
MathSciNet review:
2395162
Fulltext PDF Free Access
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Abstract: Let be a differentiably simple Noetherian commutative ring of characteristic (then is local with ). A short proof is given of the Theorem of Harper (1961) on classification of differentiably simple Noetherian commutative rings in prime characteristic. The main result of the paper is that there exists a nilpotent simple derivation of the ring such that if , then for some . The derivation is given explicitly, and it is unique up to the action of the group of ring automorphisms of . Let be the set of all such derivations. Then . The proof is based on existence and uniqueness of an iterative descent (for each ), i.e., a sequence in such that , and for all . For each , and .
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Additional Information
V. V. Bavula
Affiliation:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom
Email:
v.bavula@sheffield.ac.uk
DOI:
http://dx.doi.org/10.1090/S0002994708045674
PII:
S 00029947(08)045674
Keywords:
Simple derivation,
iterative $\delta $descent,
differentiably simple ring,
differential ideal,
coefficient field.
Received by editor(s):
February 27, 2006
Published electronically:
March 20, 2008
Article copyright:
© Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
