105 citations · 123 across the 20 of their papers we have counts for
13 papers · 1 filter
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…
Localization and test exponents for tight closure
Melvin Hochster, Craig Huneke
In this paper we study various equivalent conditions for tight closure to commute with localization. If N is a submodule of a finitely generated module M over a Noetherian commutat…
Indecomposable canonical modules and connectedness
Melvin Hochster, Craig Huneke
The purpose of this paper is to prove a generalization of Faltings' connectedness theorem which asserts that, for a complete local domain R of dimension n, the punctured spectrum o…
On the integral closure of ideals
Alberto Corso, Craig Huneke, Wolmer V. Vasconcelos
Among the several types of closures of an ideal that have been defined and studied in the past decades, the integral closure has a central place being one of the earl…
A generalized Dedekind-Mertens lemma and its converse
Alberto Corso, William Heinzer, Craig Huneke
We study content ideals of polynomials and their behavior under multiplication. We give a generalization of the Lemma of Dedekind-Mertens and prove the converse under suitable dime…
Unmixed local rings with minimal Hilbert-Kunz multiplicity are regular
Craig Huneke, Yongwei Yao
We give a new and simple proof that unmixed local rings having Hilbert-Kunz multiplicity equal to 1 must be regular.