Dumitru I. Stamate

activity

20092026

most citedThe trace of the canonical module

63 citations · 172 across the 17 of their papers we have counts for

collaborators

19 papers

math.AC2026

Nearly Gorenstein and almost symmetric properties in shifted numerical semigroups

Dumitru I. Stamate, Francesco Strazzanti

Given the integers $0 < r_{1} < \dots < r_{k}$ , we consider the shifted family of semigroups $M_{n} = ⟨ n, n + r_{1}, \dots, n + r_{k} ⟩$ , where $n > 0$ . For sufficiently large $n$ , we prove tha…

math.AC2025

Numerical semigroup tree: type-representation

Jonathan Chappelon, Jorge L. Ramírez Alfonsín, Dumitru I. Stamate

In this paper, we introduce a new depicting of the so-called numerical semigroup tree $T$ . By exploring computationally this improved picture, relying on the type notion o…

math.AC2023

The toric ring of one dimensional simplicial complexes

Antonino Ficarra, Jürgen Herzog, Dumitru I. Stamate

Let $Δ$ be a 1-dimensional simplicial complex. Then $Δ$ may be identified with a finite simple graph $G$ . In this article, we investigate the toric ring $R_{G}$ of $G$ . All graphs $G…

math.AC2022

The canonical trace of determinantal rings

Antonino Ficarra, Jürgen Herzog, Dumitru I. Stamate +1

We compute the canonical trace of generic determinantal rings and provide a sufficient condition for the trace to specialize. As an application we determine the canonical trace $\m…

math.AC2021

Stable set rings which are Gorenstein on the punctured spectrum

Takayuki Hibi, Dumitru I. Stamate

The non-Gorenstein locus of stable set rings of finite simple perfect graphs is studied. We describe combinatorially those perfect graphs whose stable set rings are Gorenstein on t…

math.AC2021

The tiny trace ideals of the canonical modules in Cohen-Macaulay rings of dimension one

Jürgen Herzog, Shinya Kumashiro, Dumitru I. Stamate

We study one-dimensional Cohen-Macaulay rings whose trace ideal of the canonical module is as small as possible. In this paper we call such rings far-flung Gorenstein rings. We inv…

math.AC2021★ 4 cited

Nearly Gorenstein rings arising from finite graphs

Takayuki Hibi, Dumitru I. Stamate

The classification of complete multipartite graphs whose edge rings are nearly Gorenstein as well as that of finite perfect graphs whose stable set rings are nearly Gorenstein is a…

math.AC2021

Gröbner-nice pairs of ideals

Mircea Cimpoeaş, Dumitru I. Stamate

We introduce the concept of a Gröbner nice pair of ideals in a polynomial ring and we present some applications.

math.AC2020★ 20 cited

Canonical trace ideal and residue for numerical semigroup rings

Jürgen Herzog, Takayuki Hibi, Dumitru I. Stamate

For a numerical semigroup ring $K [H]$ we study the trace of its canonical ideal. The colength of this ideal is called the residue of $H$ . This invariant measures how far is $H$ fro…

math.AC2020

Graded Bourbaki ideals of graded modules

Jürgen Herzog, Shinya Kumashiro, Dumitru I. Stamate

In this paper we study graded Bourbaki ideals. It is a well-known fact that for torsionfree modules over Noetherian normal domains, Bourbaki sequences exist. We give criteria in te…

math.AC2019★ 5 cited

Ulrich elements in normal simplicial affine semigroups

Jürgen Herzog, Raheleh Jafari, Dumitru I. Stamate

Let $H \subseteq N^{d}$ be a normal affine semigroup, $R = K [H]$ its semigroup ring over the field $K$ and $ω_{R}$ its canonical module. The Ulrich elements for $H$ are those $h$ …

math.AC2018★ 12 cited

Cohen-Macaulay criteria for projective monomial curves via Gröbner bases

Jürgen Herzog, Dumitru I. Stamate

We prove new characterizations based on Gröbner bases for the Cohen-Macaulay property of a projective monomial curve.

math.AC2018★ 17 cited

Betti numbers for numerical semigroup rings

Dumitru I. Stamate

We survey results related to the magnitude of the Betti numbers of numerical semigroup rings and of their tangent cones.

math.AC2017★ 1 cited

Anticanonical modules of Segre products

Viviana Ene, Jürgen Herzog, Dumitru I. Stamate

We compute the anticanonical module of the Segre product of standard graded $K$ -algebras and determine its depth.

math.AC2016★ 63 cited

The trace of the canonical module

Jürgen Herzog, Takayuki Hibi, Dumitru I. Stamate

The trace of the canonical module (the canonical trace) determines the non-Gorenstein locus of a local Cohen--Macaulay ring. We call a local Cohen--Macaulay ring nearly Gorenstein,…

math.AC2015

On the Cohen-Macaulay property for quadratic tangent cones

Dumitru I. Stamate

Let $H$ be an $n$ -generated numerical semigroup such that its tangent cone $gr_{m} K [H]$ is defined by quadratic relations. We show that if $n < 5$ then $\ope…

math.AC2015★ 7 cited

Quadratic numerical semigroups and the Koszul property

Jürgen Herzog, Dumitru I. Stamate

Let $H$ be a numerical semigroup. We give effective bounds for the multiplicity $e (H)$ when the associated graded ring $gr_{m} K [H]$ is defined by quadrics.…

math.AC2013★ 32 cited

On the defining equations of the tangent cone of a numerical semigroup ring

Jürgen Herzog, Dumitru I. Stamate

Let $a = a_{1} < \dots < a_{r}$ be a sequence of positive integers, and let $H_{a}$ denote the semigroup generated by $a_{1}, \dots, a_{r}$ . For an integer $k \geq 0$ we de…

math.AC2009★ 11 cited

Koszul incidence algebras, affine semigroups, and Stanley-Reisner ideals

Victor Reiner, Dumitru I. Stamate

We prove a theorem unifying three results from combinatorial homological and commutative algebra, characterizing the Koszul property for incidence algebras of posets and affine sem…