Right and Left Modules over the Frobenius Skew Polynomial Ring in the F-Finite Case

Details Right and Left Modules over the Frobenius Skew Polynomial Ring in the F-Finite Case Right and Left Modules over the Frobenius Skew Polynomial Ring in the F-Finite Case

2010-08-23

arxiv.org/abs/1008.3763v2

Mathematics

Commutative Algebra

16 pages, to appear in the Mathematical Proceedings of the Cambridge Philosophical Society. This revised version includes two

Scientific paper

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.

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