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Duong Thi Huong

Publications and source records attributed to Duong Thi Huong.

7 recordsLinked to original sources
arXiv2026

A sharp bound for the Frobenius test exponents in generalized Cohen-Macaulay local rings

Let $(R,\frak m)$ be a generalized Cohen-Macaulay local ring of prime characteristic $p$. In this paper we give a sharp bound for the Frobenius test exponent of parameter ideals. Namely, we prove that $$\mathrm{Fte}(R) \le \lceil \log_p(2n_0)\rceil + \mathrm{HSL}(R),$$ where $n_0$ is the integer such that $\frak m^{n_0} \, H^i_{\frak m}(R) = 0$ for all $i < \mathrm{dim}(R)$, and $\lceil x\rceil$ is the smallest integer that is greater than or equal to $x$.

math.AC↗
arXiv2025

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

Let $(R, \frak m)$ 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 $\mathrm{Fte}(R)$. We will give an upper bound for the multiplicity of Cohen-Macaulay rings in prime characteristic in terms of $\mathrm{Fte}(R),d,v$ and $s$. Our result extends the main results for Gorenstein rings due to Huneke and Watanabe.

math.AC↗
arXiv2022

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

Let $(R,\frak m)$ be an excellent generalized Cohen-Macaulay local ring of dimension $d$ that is $F$-injective on the punctured spectrum. Let $\frak q$ be a standard parameter ideal of $R$. The aim of the paper is to prove that $$\ell_R({\frak q}^F/{\frak q})\leq \sum\limits_{i=0}^{d}\binom{d}{i}\ell_R(0^F_{H^i_{\frak m}(R)}).$$ Moreover, if $\frak q$ is contained in a large enough power of $\frak m$, we have $${\frak q}^F/{\frak q} \cong \bigoplus_{i=0}^d (0^F_{H^i_{\frak m}(R)})^{\binom{d}{i}}.$$

math.AC↗
arXiv2021

Frobenius test exponent for ideals generated by filter regular sequences

Let $(R,\frak m)$ be a Noetherian local ring of prime characteristic $p>0$, and $t$ an integer such that $H_{\frak m}^j(R)/0^F_{H^j_{\frak m}(R)}$ has finite length for all $j<t$. The aim of this paper is to show that there exists an uniform bound for Frobenius test exponents of ideals generated by filter regular sequences of length at most $t$.

math.AC↗
arXiv2019

Upper bound of multiplicity in prime characteristic

Let $(R, \frak m)$ be a local ring of prime characteristic $p$ of dimension $d$ with the embedding dimension $v$. Suppose the Frobenius test exponent for parameter ideals $Fte(R)$ of $R$ is finite, and let $Q = p^{Fte(R)}$. It is shown that $$e(R) \le Q^{v-d} \binom{v}{d}.$$ We also improve our bound for $F$-nilpotent rings. Our result extends the main results of Huneke and Watanabe and of Katzman and Zhang.

math.AC↗
arXiv2018

Notes on the Frobenius test exponents

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-Lyubeznik number. Our argument is based on an isomorphism of Nagel and Schenzel on local cohomology that we will provide an elementary proof.

math.AC↗