It is shown that certain aspects of the theory of tight closure are well behaved under
localization. Let/be the parameter test ideal for R, a complete local Cohen-Macaulay ring of …

All rings in this paper are commutative with identity and have prime characteristic p.
Definitions of the terms used in this introduction can be found in Sect. 2. The main theorem …

We introduce the notion of a test exponent for tight closure and explore its relationship with
the problem of showing that tight closure commutes with localization, a long-standing open …

Let $ R $ be a reduced ring that is essentially of finite type over an excellent regular local
ring of prime characteristic. Then it is shown that the test ideal of $ R $ commutes with …

In its principal setting, tight closure is an operation perfomed on ideals in a commutative.
Noetherian ring of prime characteristic. This operation was introduced by Hochster and …

Let $ A $ be a regular local ring of positive characteristic. This paper is concerned with the
local cohomology modules of $ A $ itself, but with respect to an arbitrary ideal of $ A $. The …

This paper is concerned with tight closure in a commutative Noetherian ring R of prime
characteristic p, and is motivated by an argument of KE Smith and I. Swanson that shows …

Recently Hochster [6] has made a remarkable discovery of a procedure for con-structing
maximal Cohen-Macaulay modules over equicharacteristic local rings. The existence of …

Huge progress in the study of the homological properties of commutative rings has been
made through the use of tight closure, an idea developed by Mel Hochster and Craig …

The important ideas of reduction and integral closure of an ideal in a commutative
Noetherian ring A (with identity) were introduced by Northcott and Rees [7]; a brief and direct …