38 citations · 160 across the 19 of their papers we have counts for
28 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}…
Resurgence number of graded families of ideals
Tài Huy Hà, Arvind Kumar, Hop D. Nguyen +1
We define the resurgence and asymptotic resurgence numbers associated to a pair of graded families of ideals in a Noetherian ring. These notions generalize the well-studied resurge…
Asymptotic regularity of invariant chains of edge ideals
Do Trong Hoang, Hop D. Nguyen, Quang Hoa Tran
We study chains of nonzero edge ideals that are invariant under the action of the monoid of increasing functions on the positive integers. We prove that the sequence…
A sharp bound for the resurgence of sums of ideals
Do Van Kien, Hop Dang Nguyen, Le Minh Thuan
We prove a sharp upper bound for the resurgence of sums of ideals involving disjoint sets of variables, strengthening work of Bisui--Hà--Jayanthan--Thomas. Complete solutions are d…
On regularity and projective dimension of invariant chains of monomial ideals
Dinh Van Le, Hop D. Nguyen
Ideals in infinite-dimensional polynomial rings that are invariant under the action of the monoid of increasing functions have been extensively studied recently. Of particular inte…
Binomial expansion for saturated and symbolic powers of sums of ideals
Huy Tai Ha, A. V. Jayanthan, Arvind Kumar +1
There are two different notions for symbolic powers of ideals existing in the literature, one defined in terms of associated primes, the other in terms of minimal primes. Elaborati…
Powers of sums and their associated primes
Hop D. Nguyen, Quang Hoa Tran
Let be polynomial rings over a field , and proper homogeneous ideals. We analyze the associated primes of powers of $I+J\subseteq A\otimes_k…
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…
Regularity and Koszul property of symbolic powers of monomial ideals
Le Xuan Dung, Truong Thi Hien, Hop D. Nguyen +1
Let be a homogeneous ideal in a polynomial ring over a field. Let be the -th symbolic power of . Motivated by results about ordinary powers of , we study the…
Codimension and Projective Dimension up to Symmetry
Dinh Van Le, Uwe Nagel, Hop D. Nguyen +1
Symmetric ideals in increasingly larger polynomial rings that form an ascending chain are investigated. We focus on the asymptotic behavior of codimensions and projective dimension…
Castelnuovo-Mumford regularity up to symmetry
Dinh Van Le, Uwe Nagel, Hop D. Nguyen +1
We study the asymptotic behavior of the Castelnuovo-Mumford regularity along chains of graded ideals in increasingly larger polynomial rings that are invariant under the action of…
Homological invariants of powers of fiber products
Hop D. Nguyen, Thanh Vu
Let and be polynomial rings of positive dimensions over a field . Let be non-zero homogeneous ideals none of which contains a linear form. D…
Products of ideals of linear forms in quadric hypersurfaces
Aldo Conca, Hop D. Nguyen, Thanh Vu
Conca and Herzog proved that any product of ideals of linear forms in a polynomial ring has a linear resolution. The goal of this paper is to establish the same result for any quad…
The absolutely Koszul property of Veronese subrings and Segre products
Hop D. Nguyen
Absolutely Koszul algebras are a class of rings over which any finite graded module has a rational Poincaré series. We provide a criterion to detect non-absolutely Koszul rings. Co…
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…
Powers of sums and their homological invariants
Hop D. Nguyen, Thanh Vu
Let and be standard graded algebras over a field , and and homogeneous ideals. Denote by the sum of the extensions of and to…
Betti splittings for powers of sums of ideals
Hop D. Nguyen
Let and be standard graded polynomial rings over a field and and be non-zero, proper homogeneous ideals contained in and , respectively. Denote by th…
Linearity defect of edge ideals and Fröberg's theorem
Hop D. Nguyen, Thanh Vu
Fröberg's classical theorem about edge ideals with -linear resolution can be regarded as a classification of graphs whose edge ideals have linearity defect zero. Extending his t…
On the asymptotic behavior of the linearity defect
Hop D. Nguyen, Thanh Vu
This work concerns the linearity defect of a module over a noetherian local ring , introduced by Herzog and Iyengar in 2005, and denoted by . Roughly speaking…
Absolutely Koszul algebras and the Backelin-Roos property
Aldo Conca, Srikanth B. Iyengar, Hop D. Nguyen +1
We study absolutely Koszul algebras, Koszul algebras with the Backelin-Roos property and their behavior under standard algebraic operations. In particular, we identify some Verones…
Notes on the linearity defect and applications
Hop D. Nguyen
The linearity defect, introduced by Herzog and Iyengar, is a numerical measure for the complexity of minimal free resolutions. Employing a characterization of the linearity defect…
Koszul hypersurfaces over the exterior algebras
Hop D. Nguyen
We prove that if is an exterior algebra over a field, is a quadratic form, then is Koszul if and only if is a product of two linear forms.