### 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.

Original language | English |
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Pages (from-to) | 1-20 |

Number of pages | 20 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

DOIs | |

Publication status | Accepted/In press - Jan 27 2011 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Right and left modules over the Frobenius skew polynomial ring in the F-finite case.** / SHARP, RODNEY Y.; Yoshino, Yuji.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Right and left modules over the Frobenius skew polynomial ring in the F-finite case

AU - SHARP, RODNEY Y.

AU - Yoshino, Yuji

PY - 2011/1/27

Y1 - 2011/1/27

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=78951484286&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78951484286&partnerID=8YFLogxK

U2 - 10.1017/S0305004110000617

DO - 10.1017/S0305004110000617

M3 - Article

AN - SCOPUS:78951484286

SP - 1

EP - 20

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

ER -