Integral closure has played a role in number theory and algebraic geometry since the
nineteenth century, but a modern formulation of the concept for ideals perhaps began with …

In this paper we will study several kinds of uniform behavior in noetherian rings. This author
has felt for some time that behind the obvious finiteness condition in noetherian rings, ie, that …

These notes are based on five lectures given at the Summer School on Commutative
Algebra held at the CRM in Barcelona during July, 1996. I would like to thank the organizers …

We systematically study the intersection flatness and Ohm-Rush properties for modules over
a commutative ring, drawing inspiration from the work of Ohm and Rush and of Hochster and …

The strong uniform Artin-Rees property in codimension one Page 1 J. reine angew. Math. 527
(2000), 185Ð201 Journal fuÈr die reine und angewandte Mathematik ( Walter de Gruyter …

Let $ A $ be a noetherian ring, $ I $ an ideal of $ A $ and $ N\subset M $ finitely generated $
A $-modules. The relation type of $ I $ with respect to $ M $, denoted by ${\bf rt}\,(I; M) $, is …

We establish a uniform bound for the Castelnuovo–Mumford regularity of associated graded
rings of parameter ideals in a generalized Cohen–Macaulay ring. As consequences, we …

Uniform behavior in noetherian rings is an interesting and important subject. Several kinds
of uniform behavior in noetherian rings have been studied. For instance, Huneke [H3] has …

DESINGULARIZATIONS AND THE UNIFORM ARTIN–REES THEOREM Page 1
DESINGULARIZATIONS AND THE UNIFORM ARTIN–REES THEOREM CRAIG HUNEKE A …

The relation type question, raised by C. Huneke, asks whether for a complete
equidimensional local ring R there exists a uniform number N such that the relation type of …