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On the Hartshorne-Speiser-Lyubeznik theorem about Artinian modules with a Frobenius action

Author(s): Rodney Y. Sharp
Journal: Proc. Amer. Math. Soc. 135 (2007), 665-670.
MSC (2000): Primary 13A35, 13E10, 16S36; Secondary 13D45
Posted: August 28, 2006
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Abstract: Let $ R$ be a commutative Noetherian local ring of prime characteristic. The purpose of this paper is to provide a short proof of G. Lyubeznik's extension of a result of R. Hartshorne and R. Speiser about a module over the skew polynomial ring $ R[x,f]$ (associated to $ R$ and the Frobenius homomorphism $ f$, in the indeterminate $ x$) that is both $ x$-torsion and Artinian over $ R$.

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Additional Information:

Rodney Y. Sharp
Affiliation: Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom
Email: R.Y.Sharp@sheffield.ac.uk

DOI: 10.1090/S0002-9939-06-08606-0
PII: S 0002-9939(06)08606-0
Keywords: Commutative Noetherian ring, prime characteristic, Frobenius homomorphism, Artinian module, Frobenius skew polynomial ring
Received by editor(s): September 28, 2005
Posted: August 28, 2006
Additional Notes: The author was partially supported by the Engineering and Physical Sciences Research Council of the United Kingdom (grant number EP/C538803/1).
Communicated by: Bernd Ulrich
Copyright of article: Copyright 2006, American Mathematical Society

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