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Tight closure test exponents for certain parameter ideals
Rodney Y. Sharp
This paper is concerned with the tight closure of an ideal in a commutative Noetherian ring of prime characteristic . The formal definition requires, on the face of thin…
Uniform Behaviour of the Frobenius closures of ideals generated by regular sequences
Mordechai Katzman, Rodney Y. Sharp
This paper is concerned with ideals in a commutative Noetherian ring of prime characteristic. The main purpose is to show that the Frobenius closures of certain ideals of g…
Ideals in a perfect closure, linear growth of primary decompositions, and tight closure
Rodney Y. Sharp, Nicole Nossem
This paper is concerned with tight closure in a commutative Noetherian ring of prime characteristic , and is motivated by an argument of K. E. Smith and I. Swanson that show…
Associated primes of graded components of local cohomology modules
Markus P. Brodmann, Mordechai Katzman, Rodney Y. Sharp
The -th local cohomology module of a finitely generated graded module over a standard positively graded commutative Noetherian ring , with respect to the irrelevant ideal…
Some properties of top graded local cohomology modules
Mordechai Katzman, Rodney Y. Sharp
This first part of the paper describes the support of top graded local cohomology modules. As a corrolary one obtains a simple criteria for the vanishing of these modules and also…