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A sufficient condition for strong $ F$-regularity


Authors: Alessandro De Stefani and Luis Núñez-Betancourt
Journal: Proc. Amer. Math. Soc. 144 (2016), 21-29
MSC (2010): Primary 13A35, 13D45
DOI: https://doi.org/10.1090/proc/12676
Published electronically: June 9, 2015
MathSciNet review: 3415573
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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
Email: ad9fa@virginia.edu

Luis Núñez-Betancourt
Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22903
Email: lcn8m@virginia.edu

DOI: https://doi.org/10.1090/proc/12676
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
Article copyright: © Copyright 2015 American Mathematical Society