55 citations · 233 across the 21 of their papers we have counts for
25 papers
Saturation degree of powers of graded ideals
Le Tuan Hoa, Hop Dang Nguyen, Ngo Viet Trung
Let be a non-nilpotent graded ideal of a standard graded algebra over a Noetherian commutative ring. We show that the saturation degree sdeg is asymptotically a constant…
Regularity functions of powers of graded ideals
Le Tuan Hoa, Hop Dang Nguyen, Ngo Viet Trung
This paper studies the problem of which sequences of non-negative integers arise as the functions , , $\operatorname{reg}…
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 is asymptotically a constant, i.e. there is a number such that $\operatorname{depth} R/I^t = \opera…
Decreasing behavior of the depth functions of edge ideals
Ha Thi Thu Hien, Ha Minh Lam, Ngo Viet Trung
Let be the edge ideal of a connected non-bipartite graph and the base polynomial ring. Then and for $t \gg…
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…
Multiplicity sequence and integral dependence
Claudia Polini, Ngo Viet Trung, Bernd Ulrich +1
We prove that two arbitrary ideals in an equidimensional and universally catenary Noetherian local ring have the same integral closure if and only if they have the sa…
Depth functions of symbolic powers of homogeneous ideals
Hop Dang Nguyen, Ngo Viet Trung
This paper addresses the problem of comparing minimal free resolutions of symbolic powers of an ideal. Our investigation is focused on the behavior of the function depth R/I^(t) =…
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 , , where is a homogeneous ideal in a polynomial ring , can be any convergent…
Membership criteria and containments of powers of monomial ideals
Huy Tai Ha, Ngo Viet Trung
We present a close relationship between matching number, covering numbers and their fractional versions in combinatorial optimization and ordinary powers, integral closures of powe…
Depth and regularity modulo a principal ideal
Giulio Caviglia, Huy Tai Ha, Jürgen Herzog +3
We study the relationship between depth and regularity of a homogeneous ideal I and those of (I,f) and I:f, where f is a linear form or a monomial. Our results has several interest…
Symbolic powers of sums of ideals
Huy Tai Ha, Dang Hop Nguyen, Ngo Viet Trung +1
Let and be nonzero ideals in two Noetherian algebras and over a field . Let denote the ideal generated by and in . We prove the follo…
Toward a Theory of Monomial Preorders
Gregor Kemper, Ngo Viet Trung, Nguyen Thi Van Anh
In this paper we develop a theory of monomial preorders, which differ from the classical notion of monomial orders in that they allow ties between monomials. Since for monomial pre…
Castelnuovo-Mumford regularity and Ratliff-Rush closure
Trung Thanh Dinh, Maria Evelina Rossi, Ngo Viet Trung
We establish strong relationships between the Castelnuovo-Mumford regularity and the Ratliff-Rush closure of an ideal. Our results have several interesting consequences on the comp…
Associated primes of powers of edge ideals and ear decompositions of graphs
Ha Minh Lam, Ngo Viet Trung
In this paper, we give a complete description of the associated primes of every power of the edge ideal in terms of generalized ear decompositions of the graph. This result establi…
Depth and regularity of powers of sums of ideals
Huy Tai Ha, Ngo Viet Trung, Tran Nam Trung
Given arbitrary homogeneous ideals and in polynomial rings and over a field , we investigate the depth and the Castelnuovo-Mumford regularity of powers of the su…
Saturation and associated primes of powers of edge ideals
Ha Thi Thu Hien, Ha Minh Lam, Ngo Viet Trung
For the edge ideal I of an arbitrary simple graph G we describe the monomials of the saturation of a power of I in terms of (vertex) weighted graphs associated with the monomials.…
The Bhattacharya function of complete monomial ideals in two variables
Hong Ngoc Binh, Ngo Viet Trung
We give explicit formulas for the Bhattacharya function of m-primary complete monomial ideals in two variables in terms of the vertices of the Newton polyhedra or in terms of the d…
Absolutely superficial sequences
Ngo Viet Trung
Absolutely superficial sequences was introduced by P. Schenzel in order to study generalized Cohen-Macaulay (resp. Buchsbaum) modules. For an arbitrary local ring, they turned out…
On the associated primes and the depth of the second power of squarefree monomial ideals
Naoki Terai, Ngo Viet Trung
We present combinatorial characterizations for the associated primes of the second power of squarefree monomial ideals and criteria for this power to have positive depth or depth g…
Krull dimension and Monomial Orders
Gregor Kemper, Ngo Viet Trung
We introduce the notion of independent sequences with respect to a monomial order by using the least terms of polynomials vanishing at the sequence. Our main result shows that the…
Cohen-Macaulayness of large powers of Stanley-Reisner ideals
Naoki Terai, Ngo Viet Trung
We prove that for m > 2, the m-th symbolic power of a Stanley-Reisner ideal is Cohen-Macaulay if and only if the simplicial complex is a matroid. Similarly, the m-th ordinary power…
Equality of ordinary and symbolic powers of Stanley-Reisner ideals
Ngo Viet Trung, Tran Manh Tuan
This paper studies properties of simplicial complexes for which the m-th symbolic power of the Stanley-Reisner ideal equals to the m-th ordinary power for a given m > 1. The main r…
Cohen-Macaulayness of powers of two-dimensional squarefree monomial ideals
Nguyen Cong Minh, Ngo Viet Trung
Two-dimensional squarefree monomial ideals can be seen as the Stanley-Reisner ideals of graphs. The main results of this paper are combinatorial characterizations for the Cohen-Mac…
Cohen-Macaulayness of monomial ideals and symbolic powers of Stanley-Reisner ideals
Nguyen Cong Minh, Ngo Viet Trung
We present criteria for the Cohen-Macaulayness of a monomial ideal in terms of its primary decomposition. These criteria allow us to use tools of graph theory and of linear program…