13 citations · 19 across the 10 of their papers we have counts for
14 papers
Nearly Gorenstein and almost symmetric properties in shifted numerical semigroups
Dumitru I. Stamate, Francesco Strazzanti
Given the integers , we consider the shifted family of semigroups , where . For sufficiently large , we prove tha…
Some classes of one-dimensional rings characterized by their reflexive ideals
Pietro Campochiaro, Marco D'Anna, Francesco Strazzanti
We study reflexive ideals in one-dimensional Cohen-Macaulay local rings, providing characterizations of almost Gorenstein rings, rings with minimal multiplicity, and Arf rings, whi…
Nearly Gorenstein numerical semigroups with five generators have bounded type
Alessio Moscariello, Francesco Strazzanti
We prove that the type of nearly Gorenstein numerical semigroups minimally generated by integers is bounded. In particular, if such a semigroup is not almost symmetric, then it…
On nearly Gorenstein affine semigroups
Raheleh Jafari, Francesco Strazzanti, Santiago Zarzuela Armengou
We describe the canonical module of a simplicial affine semigroup ring and its trace ideal. As a consequence, we characterize when is nearly Gorenst…
Simplicial affine semigroups with monomial minimal reduction ideals
Marco D'Anna, Raheleh Jafari, Francesco Strazzanti
We characterize when the monomial maximal ideal of a simplicial affine semigroup ring has a monomial minimal reduction. When this is the case, we study the Cohen-Macaulay and Goren…
Nearly Gorenstein cyclic quotient singularities
Alessio Caminata, Francesco Strazzanti
We investigate the nearly Gorenstein property among -dimensional cyclic quotient singularities , where is an algebraically closed field and $G\…
When is an almost Gorenstein ring?
Marco D'Anna, Francesco Strazzanti
Given a one-dimensional Cohen-Macaulay local ring , we prove that it is almost Gorenstein if and only if is a canonical module of the ring $\math…
Almost canonical ideals and GAS numerical semigroups
Marco D'Anna, Francesco Strazzanti
We propose the notion of GAS numerical semigroup which generalizes both almost symmetric and 2-AGL numerical semigroups. Moreover, we introduce the concept of almost canonical idea…
Nearly Gorenstein vs almost Gorenstein affine monomial curves
Alessio Moscariello, Francesco Strazzanti
We extend some results on almost Gorenstein affine monomial curves to the nearly Gorenstein case. In particular, we prove that the Cohen-Macaulay type of a nearly Gorenstein monomi…
The Hilbert-Kunz function of some quadratic quotients of the Rees algebra
Francesco Strazzanti, Santiago Zarzuela Armengou
Given a commutative local ring and an ideal of , a family of quotients of the Rees algebra has been recently studied as a unified approach to the N…
Tangent cones of monomial curves obtained by numerical duplication
Marco D'Anna, Raheleh Jafari, Francesco Strazzanti
Given a numerical semigroup ring , an ideal of and an odd element , the numerical duplication is a numerical semigroup, whose ass…
New algebraic properties of quadratic quotients of the Rees algebra
Marco D'Anna, Francesco Strazzanti
We study some properties of a family of rings that are obtained as quotients of the Rees algebra associated with a ring and an ideal . In particular, we give a…
One-dimensional Gorenstein local rings with decreasing Hilbert function
Anna Oneto, Francesco Strazzanti, Grazia Tamone
In this paper we solve a problem posed by M.E. Rossi: {\it Is the Hilbert function of a Gorenstein local ring of dimension one not decreasing? } More precisely, for any integer $h>…
Families of Gorenstein and almost Gorenstein rings
Valentina Barucci, Marco D'Anna, Francesco Strazzanti
Starting with a commutative ring and an ideal , it is possible to define a family of rings , with , as quotients of the Rees algebra $\oplus_{n \geq 0…