Test ideals in local rings
KE Smith - Transactions of the American Mathematical Society, 1995 - ams.org
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 …
localization. Let/be the parameter test ideal for R, a complete local Cohen-Macaulay ring of …
[PDF][PDF] Tight closure of parameter ideals
KE Smith - Inventiones mathematicae, 1994 - researchgate.net
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 …
Definitions of the terms used in this introduction can be found in Sect. 2. The main theorem …
Localization and test exponents for tight closure.
M Hochster, C Huneke - Michigan Mathematical Journal, 2000 - projecteuclid.org
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 …
the problem of showing that tight closure commutes with localization, a long-standing open …
On the commutation of the test ideal with localization and completion
G Lyubeznik, K Smith - Transactions of the American Mathematical Society, 2001 - ams.org
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 …
ring of prime characteristic. Then it is shown that the test ideal of $ R $ commutes with …
Tight closure in graded rings
KE Smith - Journal of Mathematics of Kyoto University, 1997 - projecteuclid.org
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 …
Noetherian ring of prime characteristic. This operation was introduced by Hochster and …
Bass numbers of local cohomology modules
CL Huneke, RY Sharp - Transactions of the American Mathematical Society, 1993 - ams.org
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 …
local cohomology modules of $ A $ itself, but with respect to an arbitrary ideal of $ A $. The …
Ideals in a perfect closure, linear growth of primary decompositions, and tight closure
R Sharp, N Nossem - Transactions of the American Mathematical Society, 2004 - ams.org
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 …
characteristic p, and is motivated by an argument of KE Smith and I. Swanson that shows …
[PDF][PDF] A representation theorem for complete local rings
P Griffith - Journal of Pure and Applied Algebra, 1976 - core.ac.uk
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 …
maximal Cohen-Macaulay modules over equicharacteristic local rings. The existence of …
[引用][C] Extensions of plus closure
RC Heitmann - Journal of Algebra, 2001 - Elsevier
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 …
made through the use of tight closure, an idea developed by Mel Hochster and Craig …
[引用][C] Integral closures of ideals relative to local cohomology modules over quasi-unmixed local rings
RY Sharp, Y Tiraş, M Yassi - Journal of the London Mathematical …, 1990 - academic.oup.com
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 …
Noetherian ring A (with identity) were introduced by Northcott and Rees [7]; a brief and direct …