11 citations · 18 across the 13 of their papers we have counts for
17 papers
Artinian Gorenstein algebras with binomial Macaulay dual generator
Nasrin Altafi, Rodica Dinu, Sara Faridi +4
This paper initiates a systematic study for key properties of Artinian Gorenstein \(K\)-algebras having binomial Macaulay dual generators. In codimension 3, we demonstrate that all…
New families of Artinian Gorenstein algebras with the weak Lefschetz property
Nasrin Altafi, Rodica Dinu, Shreedevi K. Masuti +3
We construct new families of Artinian Gorenstein graded -algebras of arbitrary codimension having binomial Macaulay dual generators and satisfying the weak or the strong Lefsche…
Jordan degree type for codimension three Gorenstein algebras of small Sperner number
Nancy Abdallah, Nasrin Altafi, Anthony Iarrobino +1
The Jordan type of a linear form acting on a graded Artinian algebra over a field is the partition describing the Jordan block decomposition of the…
Betti numbers for connected sums of graded Gorenstein artinian algebras
Nasrin Altafi, Roberta Di Gennaro, Federico Galetto +5
The connected sum construction, which takes as input Gorenstein rings and produces new Gorenstein rings, can be considered as an algebraic analogue for the topological construction…
Jordan type of an Artinian algebra, a survey
Nasrin Altafi, Anthony Iarrobino, Pedro Macias Marques
We consider Artinian algebras over a field , both graded and local algebras. The Lefschetz properties of graded Artinian algebras have been long studied, but more r…
Forcing the weak Lefschetz property for equigenerated monomial ideals
Nasrin Altafi, Samuel Lundqvist
We classify the minimal number of generators of artinian equigenerated monomial ideals such that is forced to have the weak Lefschetz property.
A note on Jordan types and Jordan degree types
Nasrin Altafi
We discuss whether the Jordan degree type encodes \break more information about graded artinian Gorenstein algebras than the Jordan type for linear forms. We show that in codimensi…
Hilbert functions and Jordan type of Perazzo Artinian algebras
Nancy Abdallah, Nasrin Altafi, Pietro De Poi +6
We study Hilbert functions, Lefschetz properties, and Jordan type of Artinian Gorenstein algebras associated to Perazzo hypersurfaces in projective space. The main focus lies on Pe…
Lefschetz properties of some codimension three Artinian Gorenstein algebras
Nancy Abdallah, Nasrin Altafi, Anthony Iarrobino +2
Codimension two Artinian algebras have the strong and weak Lefschetz properties provided the characteristic is zero or greater than the socle degree. It is open to what extent…
Monomial ideals and the failure of the Strong Lefschetz property
Nasrin Altafi, Samuel Lundqvist
We give a sharp lower bound for the Hilbert function in degree of artinian quotients failing the Strong Lefschetz property, where is a monomial id…
Jordan types with small parts for Artinian Gorenstein algebras of codimension three
Nasrin Altafi
We study Jordan types of linear forms for graded Artinian Gorenstein algebras having arbitrary codimension. We introduce rank matrices of linear forms for such algebras that repres…
Hilbert Functions of Artinian Gorenstein algebras with the Strong Lefschetz Property
Nasrin Altafi
We prove that a sequence of non-negative integers is the Hilbert function of some Artinian Gorenstein algebra with the strong Lefschetz property if and only if it is an SI-sequ…
Number of generators of ideals in Jordan cells of the family of graded Artinian algebras of height two
Nasrin Altafi, Anthony Iarrobino, Leila Khatami +1
We let be a standard graded Artinian algebra quotient of , the polynomial ring in two variables over a field by an ideal , and let be its v…
Complete intersection Jordan types in height two
Nasrin Altafi, Anthony Iarrobino, Leila Khatami
We determine every Jordan type partition that occurs as the Jordan block decomposition for the multiplication map by a linear form in a height two homogeneous complete intersection…
The weak Lefschetz property of equigenerated monomial ideals
Nasrin Altafi, Mats Boij
We determine a sharp lower bound for the Hilbert function in degree of a monomial algebra failing the weak Lefschetz property over a polynomial ring with variables and gene…
Lefschetz properties of monomial ideals with almost linear resolution
Nasrin Altafi, Navid Nemati
We study the WLP and SLP of artinian monomial ideals in via studying their minimal free resolutions. We study the Lefschetz properties of such ideals…
Free resolution of powers of monomial ideals and Golod rings
Nasrin Altafi, Navid Nemati, S. A. Seyed Fakhari +1
Let be the polynomial ring over a field . In this paper we present a criterion for componentwise linearity of powers of monomial ideal…