8 citations · 22 across the 19 of their papers we have counts for
28 papers
Buchsbaum modules and parameter ideals under flat extensions
Nguyen Thi Hong Loan, Le Thanh Nhan, Pham Hung Quy
Let and be commutative Noetherian local rings, let be a flat local homomorphism. In this paper, we first characterize the ascent and descen…
A sharp bound for the Frobenius test exponents in generalized Cohen-Macaulay local rings
Duong Thi Huong, Pham Hung Quy
Let be a generalized Cohen-Macaulay local ring of prime characteristic . In this paper we give a sharp bound for the Frobenius test exponent of parameter ideals. N…
On the perturbations of Noetherian local domains
Hong Duc Nguyen, Hop D. Nguyen, Pham Hung Quy
We study how the properties of being reduced, integral domain, and normal, behave under small perturbations of the defining equations of a noetherian local ring. It is not hard to…
Colength, multiplicity, and ideal closure operations II
Linquan Ma, Pham Hung Quy, Ilya Smirnov
Let be a Noetherian local ring. This paper concerns several extremal invariants arising from the study of the relation between colength and (Hilbert--Samuel or…
Vanishing and non-negativity of the first normal Hilbert coefficient
Linquan Ma, Pham Hung Quy
Let be a Noetherian local ring such that is reduced. We prove that, when is , if there exists a parameter ideal s…
Tight Hilbert Polynomial and F-rational local rings
Saipriya Dubey, Pham Hung Quy, Jugal Verma
Let be a Noetherian local ring of prime characteristic and be an -primary parameter ideal. We give criteria for F-rationality of using…
A Buchsbaum theory for tight closure
Linquan Ma, Pham Hung Quy
A Noetherian local ring is called Buchsbaum if the difference , where is an ideal generated by a system o…
When does a perturbation of the equations preserve the normal cone
Pham Hung Quy, Ngo Viet Trung
Let be a local ring and two arbitrary ideals of . Let denote the associated ring of with respect to , which correspo…
Small perturbations in generalized Cohen-Macaulay local rings
Pham Hung Quy, Van Duc Trung
Let be a generalized Cohen-Macaulay local ring of dimension , and a part of system of parameters of . In this paper we give explicit numbers…
Uniform Annihilators of Systems of parameters
Pham Hung Quy
In this paper we give uniform annihilators for some relations of all systems of parameters in a local ring. Our results provide simple proofs for some classical results.
Colength, multiplicity, and ideal closure operations
Linquan Ma, Pham Hung Quy, Ilya Smirnov
In a formally unmixed Noetherian local ring, if the colength and multiplicity of an integrally closed ideal agree, then is regular. We deduce this using the relationship betwee…
Nilpotence of Frobenius actions on local cohomology and Frobenius closure of ideals
Thomas Polstra, Pham Hung Quy
The study of Frobenius actions on local cohomology modules over a local ring of prime characteristic has interesting connections with the theory of tight closure. This paper establ…
Notes on the Frobenius test exponents
Duong Thi Huong, Pham Hung Quy
In this paper we show that the Frobenius test exponent for parameter ideals of a local ring of prime characteristic is always bigger than or equal to its Hartshorne-Speiser-Lyubezn…
Tight closure of parameter ideals in local rings -rational on the punctured spectrum
Pham Hung Quy
Let be an excellent equidimensional local ring of characteristic . The aim of this paper is to show that does not…
On the structure of finitely generated modules and the unmixed degrees
Nguyen Tu Cuong, Pham Hung Quy
Let be a homomorphic image of a Cohen-Macaulay local ring and a finitely generated -module. We use the splitting of local cohomology to shed a new light on th…
On the length function of saturations of ideal powers
Doan Trung Cuong, Pham Hong Nam, Pham Hung Quy
For an ideal in a local ring $(R, \fm)$, we prove that the integer-valued function $\ell_R(H^0_\fm(R/I^{n+1}))$ is a polynomial for big enough if either is a principle…
On the limit closure of a sequence of elements in local rings
Nguyen Tu Cuong, Pham Hung Quy
We present a systematic study for the limit closure of a sequence of elements (eg. a system of of parameters) in a local ring. Firstly, we…
Frobenius actions on local cohomology modules and deformation
Linquan Ma, Pham Hung Quy
Let be a Noetherian local ring of characteristic . We introduce and study -full and -anti-nilpotent singularities, both are defined in terms of the Frobenius act…
-injectivity and Frobenius closure of ideals in Noetherian rings of characteristic
Pham Hung Quy, Kazuma Shimomoto
The main aim of this article is to study the relation between -injective singularity and the Frobenius closure of parameter ideals in Noetherian rings of positive characteristic…
Injective modules and torsion functors
Pham Hung Quy, Fred Rohrer
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 t…
Some results on local cohomology of polynomial and formal power series rings: the one dimensional case
Pham Hung Quy
In this paper, we prove several results on the finiteness of local cohomology of polynomial and formal power series rings. In particular, we give a partial affirmative answer for a…
On the vanishing of local cohomology of the absolute integral closure in positive characteristic
Pham Hung Quy
The aim of this paper is to extend the main result of C. Huneke and G. Lyubeznik in [Adv. Math. 210 (2007), 498--504] to the class of rings that are images of Cohen-Macaulay local…
Localization at countably infinitely many prime ideals and applications
Kamal Bahmanpour, Pham Hung Quy
In this paper we present a technical lemma about localization at countable infinitely many prime ideals. We apply this lemma to get many results about the finiteness of associated…
A study of the length function of generalized fractions of modules
Marcel Morales, Pham Hung Quy
Let be a Noetherian local ring and a finitely generated -module of dimension . Let be a system of parameters of and $\u…