• The F-signature and strong F-regularity 

    Aberbach, Ian M.; Leuschke, Graham J. (2002-11)
    We show that the F-signature of a local ring of characteristic p, defined by Huneke and Leuschke, is positive if and only if the ring is strongly F-regular.
  • The structure of F-pure rings 

    Aberbach, Ian M.; Enescu, Florian (2003-10)
    For a reduced F-finite ring R of characteristic p >0 and q=p^e one can write R^{1/q} = R^{a_q} \oplus M_q, where M_q has no free direct summands over R. We investigate the structure of F-finite, F-pure rings R by studying ...
  • When does the F-signature exist? 

    Aberbach, Ian M.; Enescu, Florian (2005-02)
    We show that the F-signature of an F-finite local ring R of characteristic p > 0 exists when R is either the localization of an N-graded ring at its irrelevant ideal or Q-Gorenstein on its punctured spectrum. This extends ...