Simple derivations of differentiably simple Noetherian commutative rings in prime characteristic

Author:
V. V. Bavula

Journal:
Trans. Amer. Math. Soc. **360** (2008), 4007-4027

MSC (2000):
Primary 13N15, 13A35, 16W25

DOI:
https://doi.org/10.1090/S0002-9947-08-04567-4

Published electronically:
March 20, 2008

MathSciNet review:
2395162

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-08-04567-4

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.