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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A sufficient condition for strong $F$-regularity
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by Alessandro De Stefani and Luis Núñez-Betancourt PDF
Proc. Amer. Math. Soc. 144 (2016), 21-29 Request permission

Abstract:

Let $(R,\mathfrak {m},K)$ be an $F$-finite Noetherian local ring which has a canonical ideal $I \subsetneq R$. We prove that if $R$ is $S_2$ and $H^{d-1}_{\mathfrak {m}}(R/I)$ is a simple $R\{F\}$-module, then $R$ is a strongly $F$-regular ring. In particular, under these assumptions, $R$ is a Cohen-Macaulay normal domain.
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Additional Information
  • Alessandro De Stefani
  • Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22903
  • MR Author ID: 1053917
  • Email: ad9fa@virginia.edu
  • Luis Núñez-Betancourt
  • Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22903
  • MR Author ID: 949465
  • Email: lcn8m@virginia.edu
  • Received by editor(s): October 13, 2014
  • Received by editor(s) in revised form: November 21, 2014
  • Published electronically: June 9, 2015
  • Communicated by: Irena Peeva
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 21-29
  • MSC (2010): Primary 13A35, 13D45
  • DOI: https://doi.org/10.1090/proc/12676
  • MathSciNet review: 3415573