2 citations · 3 across the 9 of their papers we have counts for
9 papers
When does the F-signature exist?
Ian M. Aberbach, Florian Enescu
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 -graded ring at its irrelevant ideal or $…
Homology multipliers and the relation type of parameter ideals
Ian M. Aberbach, Laura Ghezzi, Huy Tai Ha
We study the relation type question, raised by C. Huneke, which asks whether for a complete equidimensional local ring R there exists a uniform bound for the relation type of param…
The Structure of F-Pure Rings
Ian M. Aberbach, Florian Enescu
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 structur…
The vanishing of Tor_1^R(R^+,k) implies that R is regular
Ian M. Aberbach
Let (R,m,k) be an excellent local ring of positive prime characteristic. We show that if Tor_1^R(R^+,k) = 0 then R is regular. This improves a result of Schoutens, in which the add…
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…