Trung Nam Tran

activity

20122023

most citedDepth and regularity of powers of sums of ideals

52 citations · 186 across the 10 of their papers we have counts for

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9 papers · 1 filter

math.AC2023

A general formula for the index of depth stability of edge ideals

Ha Minh Lam, Ngo Viet Trung, Tran Nam Trung

By a classical result of Brodmann, the function $depth R / I^{t}$ is asymptotically a constant, i.e. there is a number $s$ such that $\operatorname{depth} R/I^t = \opera…

math.AC2019★ 14 cited

Depth functions of powers of homogeneous ideals

Huy Tai Ha, Hop Dang Nguyen, Ngo Viet Trung +1

We settle a conjecture of Herzog and Hibi, which states that the function depth $S / Q^{n}$ , $n \geq 1$ , where $Q$ is a homogeneous ideal in a polynomial ring $S$ , can be any convergent…

math.AC2019★ 15 cited

Regularity and Koszul property of symbolic powers of monomial ideals

Le Xuan Dung, Truong Thi Hien, Hop D. Nguyen +1

Let $I$ be a homogeneous ideal in a polynomial ring over a field. Let $I^{(n)}$ be the $n$ -th symbolic power of $I$ . Motivated by results about ordinary powers of $I$ , we study the…

math.AC2017★ 38 cited

Symbolic powers of sums of ideals

Huy Tai Ha, Dang Hop Nguyen, Ngo Viet Trung +1

Let $I$ and $J$ be nonzero ideals in two Noetherian algebras $A$ and $B$ over a field $k$ . Let $I + J$ denote the ideal generated by $I$ and $J$ in $A \otimes_{k} B$ . We prove the follo…

math.AC2016★ 36 cited

Stability of Depths of Powers of Edge Ideals

Tran Nam Trung

Let $G$ be a graph and let $I := I (G)$ be its edge ideal. In this paper, we provide an upper bound of $n$ from which $\depth R/ I(G)^n$ is stationary, and compute this limit expli…

math.AC2015★ 27 cited

A Characterization of Triangle-free Gorenstein graphs and Cohen-Macaulayness of second powers of edge ideals

Do Trong Hoang, Tran Nam Trung

We graph-theoretically characterize triangle-free Gorenstein graphs $G$ . As an application, we classify when $I (G)^{2}$ is Cohen-Macaulay.

math.AC2015★ 52 cited

Depth and regularity of powers of sums of ideals

Huy Tai Ha, Ngo Viet Trung, Tran Nam Trung

Given arbitrary homogeneous ideals $I$ and $J$ in polynomial rings $A$ and $B$ over a field $k$ , we investigate the depth and the Castelnuovo-Mumford regularity of powers of the su…

math.AC2014

Regularity of powers of forests and cycles

Selvi Kara, Huy Tai Ha, Tran Nam Trung

Let G be a graph and let I = I(G) be its edge ideal. In this paper, when G is a forest or a cycle, we explicitly compute the regularity of I^s for all s > 0. In particular, for the…

math.AC2012★ 2 cited

Cohen-Macaulay graphs with large girth

Dô Trong Hoang, Nguyên Cong Minh, Trân Nam Trung

We classify Cohen-Macaulay graphs of girth at least $5$ and planar Gorenstein graphs of girth at least $4$ . Moreover, such graphs are also vertex decomposable.