Pham Hung Quy

activity

20162026

most citedOn the associated primes of local cohomology

2 citations · 4 across the 9 of their papers we have counts for

collaborators

14 papers

math.GR2026

Frobenius numbers and the first Hilbert coefficients of certain numerical semigroup rings

Do Van Kien, Pham Hung Quy

Let $a, b$ be positive integers. In this note, we study the numerical semigroup $H = ⟨ a, a + 1, b ⟩$ and and the associated numerical semigroup ring $R = k [[H]]$ . Under the certai…

math.AC2025

The Depth Formula for modules over quotients of Gorenstein rings

Tran Nguyen An, Pham Hung Quy

A foundational result by C. Huneke and V. Trivedi provides a formula for the depth of an ideal in terms of height, computed over a finite set of prime ideals, for rings that are ho…

math.AC2025

Upper bound of multiplicity in Cohen-Macaulay rings of prime characteristic

Duong Thi Huong, Pham Hung Quy

Let $(R, m)$ be a local ring of prime characteristic $p$ and of dimension $d$ with the embedding dimension $v$ , type $s$ and the Frobenius test exponent for parameter ideals…

math.AC2022

On the Frobenius closure of parameter ideals when the ring is F-injective on the punctured spectrum

Duong Thi Huong, Pham Hung Quy

Let $(R, m)$ be an excellent generalized Cohen-Macaulay local ring of dimension $d$ that is $F$ -injective on the punctured spectrum. Let $q$ be a standard parameter idea…

math.NT2021

A Note on Je{ś}manowicz' Conjecture for Non-primitive Pythagorean Triples

Van Thien Nguyen, Viet Kh. Nguyen, Pham Hung Quy

Let $(a, b, c)$ be a primitive Pythagorean triple parameterized as $a = u^{2} - v^{2}, b = 2 uv, c = u^{2} + v^{2}$ ,\ where $u > v > 0$ are co-prime and not of the same parity. In 1956, L. Je{ś}manowic…

math.AC2021

Frobenius test exponent for ideals generated by filter regular sequences

Duong Thi Huong, Pham Hung Quy

Let $(R, m)$ be a Noetherian local ring of prime characteristic $p > 0$ , and $t$ an integer such that $H_{m}^{j} (R) / 0_{H_{m}^{j} (R)}^{F}$ has finite length for all $j < t$ .…

math.AC2019

Asymptotic Lech's inequality

Craig Huneke, Linquan Ma, Pham Hung Quy +1

We explore the classical Lech's inequality relating the Hilbert--Samuel multiplicity and colength of an $m$ -primary ideal in a Noetherian local ring $(R, m)$ .…

math.AC2019★ 1 cited

Filter regular sequence under small perturbations

Linquan Ma, Pham Hung Quy, Ilya Smirnov

We answer affirmatively a question of Srinivas--Trivedi: in a Noetherian local ring $(R, m)$ , if $I = (f_{1}, \dots, f_{r})$ is an ideal generated by a filter-regular sequence an…

math.AC2019

On the index of reducibility of parameter ideals: The stable and limit values

Nguyen Tu Cuong, Pham Hung Quy

Let $(R, m)$ be a Noetherian local ring and $M$ a finitely generated $R$ -module of dimension $d$ . A famous result of Northcott says that if $M$ is Cohen-Macaulay, then the in…

math.AC2019

Upper bound of multiplicity in prime characteristic

Duong Thi Huong, Pham Hung Quy

Let $(R, m)$ be a local ring of prime characteristic $p$ of dimension $d$ with the embedding dimension $v$ . Suppose the Frobenius test exponent for parameter ideals $F t e (R)$ …

math.AC2018★ 1 cited

Lech's inequality, the Stückrad--Vogel conjecture, and uniform behavior of Koszul homology

Patricia Klein, Linquan Ma, Pham Hung Quy +2

Let $(R, m)$ be a Noetherian local ring, and let $M$ be a finitely generated $R$ -module of dimension $d$ . We prove that the set $\left\{\frac{l(M/IM)}{e(I, M)} \right\}_{…

math.AC2018

On the uniform bound of Frobenius test exponents

Pham Hung Quy

In this paper we prove the existence of a uniform bound for Frobenius test exponents for parameter ideals of a local ring $(R, m)$ of prime characteristic in the following ca…

math.AC2016

On the index of reducibility of powers of a standard parameter ideal

Nguyen Tu Cuong, Pham Hung Quy, Hoang Le Truong

In this paper we study the index of reducibility of powers of a standard parameter ideal. An explicit formula is proved for the extremely case. We apply the main result to compute…

math.AC2016★ 2 cited

On the associated primes of local cohomology

Hailong Dao, Pham Hung Quy

Let $R$ be a commutative Noetherian ring of prime characteristic $p$ . In this paper we give a short proof using filter regular sequences that the set of associated prime ideals of…