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Right and left modules over the Frobenius skew polynomial ring in the F-finite case

Published online by Cambridge University Press:  27 January 2011

RODNEY Y. SHARP  and
YUJI YOSHINO
RODNEY Y. SHARP
Affiliation:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH. e-mail: R.Y.Sharp@sheffield.ac.uk
YUJI YOSHINO
Affiliation:
Department of Mathematics, Faculty of Science, Okayama University, Tsushima-Naka 3-1-1, Okayama 700-8530, Japan. e-mail: yoshino@math.okayama-u.ac.jp
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Abstract

The main purposes of this paper are to establish and exploit the result that, over a complete (Noetherian) local ring R of prime characteristic for which the Frobenius homomorphism f is finite, the appropriate restrictions of the Matlis-duality functor provide an equivalence between the category of left modules over the Frobenius skew polynomial ring R[x, f] that are Artinian as R-modules and the category of right R[x, f]-modules that are Noetherian as R-modules.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 150 , Issue 3 , May 2011 , pp. 419 - 438
Copyright
Copyright © Cambridge Philosophical Society 2011

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