2 citations · 3 across the 11 of their papers we have counts for
5 papers · 1 filter
The depth of the associated graded ring of ideals with any reduction number
Ian Aberbach, Laura Ghezzi, Huy Tai Ha
Let R be a local Cohen-Macaulay ring, let I be an R-ideal, and let G be the associated graded ring of I. We give an estimate for the depth of G when G is not necessarily Cohen-Maca…
F-rational rings and the integral closures of ideals
Ian M. Aberbach, Craig Huneke
We show in this paper that the Briancon-Skoda theorem holds for all ideals in F-rational rings of positive prime characteristic, and also in rings with rational singularities which…
Test ideals and flat base change problems in tight closure theory
Ian M. Aberbach, Florian Enescu
Test ideals are an important concept in tight closure theory and their behavior via flat base change can be very difficult to understand. Our paper presents results regarding this…
Extension of weakly and strongly F-regular rings by flat maps
Ian M. Aberbach
Let (R,m) -> (S,n) be a flat local homomorphism of excellent local rings. We investigate the conditions under which the weak or strong F-regularity of R passes to S. We show that i…
The F-signature and strong F-regularity
Ian M. Aberbach, Graham J. Leuschke
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.