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

 

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


Author: Rodney Y. Sharp
Journal: Proc. Amer. Math. Soc. 135 (2007), 665-670
MSC (2000): Primary 13A35, 13E10, 16S36; Secondary 13D45
Published electronically: August 28, 2006
MathSciNet review: 2262861
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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: http://dx.doi.org/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
Published electronically: 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
Article copyright: © Copyright 2006 American Mathematical Society