Pham Hung Quy

Injective modules and torsion functors

ABSTRACT A commutative ring is said to have ITI with respect to an ideal 𝔞 if the 𝔞-torsion functor preserves injectivity of modules. Classes of rings with ITI or without ITI with respect to certain sets of ideals are identified. Behavior of ITI under formation of rings of fractions, tensor products, and idealization is studied. Applications to local cohomology over non-noetherian rings are given.

A Remark on the Finiteness Dimension

Let 𝔞 be an ideal of a commutative Noetherian ring R and M a finitely generated R-module. The finiteness dimension of M relative to 𝔞 is defined by where is the i-th local cohomology with respect to 𝔞. The aim of this paper is to show that if x 1,…, x t is an 𝔞-filter regular sequence of M with t ≤ f 𝔞(M), then the set is finite.

On the uniform bound of Frobenius test exponents

In this paper we prove the existence of a uniform bound for Frobenius test exponents for parameter ideals of a local ring

A Study of the Length Function of Generalized Fractions of Modules

(R, \frak m)

Localization at countably infinitely many prime ideals and applications

of prime characteristic in the following cases: (1)

On the finiteness of associated primes of local cohomology modules

R

A splitting theorem for local cohomology and its applications

is generalized Cohen-Macaulay. Our proof is much more simpler than the original proof of Huneke, Katzman, Sharp and Yao, (2) The Frobenius actions on all lower local cohomologies

Attached primes of local cohomology modules under localization and completion

H^i_{\frak m}(R)

F-injectivity and Frobenius closure of ideals in Noetherian rings of characteristic p > 0 ☆

,

On the limit closure of a sequence of elements in local rings

i < \dim R