10 citations · 21 across the 18 of their papers we have counts for
20 papers
Associated primes, witnesses, and omega invariants of monomial ideals
Jacob Miller, Mehrdad Nasernejad, Ştefan O. Tohǎneanu
We introduce and study the omega invariant of a proper ideal in a Noetherian commutative ring, defined as the number of associated primes of the ideal. Our main objective is to inv…
On the existence of the maximal ideal in the set of associated primes of monomial ideals
M. Cimpoeaş, M. Nasernejad, A. A. Qureshi
In this paper, we investigate the behavior of associated primes of powers of monomial ideals, with particular emphasis on the presence of the maximal ideal and the phenomenon of fl…
Linear representation of groups associated to graphs
Alain Bretto, Alain Faisant, Neda Moradi +1
In this article, we introduce a group linear representation associated to a graph. We study this representation as well as the canonical decomposition of the associated module. A c…
Strong persistence index and fluctuations in colon powers of monomial ideals
Mehrdad Nasernejad, Jonathan Toledo
Let be an ideal in a commutative Noetherian ring . We say that a positive integer is the strong persistence index of if is the smallest integer such th…
Asymptotic Properties of Filtrations of Ideals
Mehrdad Nasernejad, Jonathan Toledo
We introduce a unified framework for studying persistence phenomena in commutative algebra via filtrations of ideals. For a filtration , w…
Demotions of ideals in commutative rings with applications to normally torsion-freeness
Mehrdad Nasernejad, Jonathan Toledo
Let J \subseteq I be ideals in a commutative Noetherian ring R, and r,s \geq 0. We say that J is a demotion of I if I^r J^s = I^{r+s} \cap J^s for all r,s \geq 0. In this paper, we…
Criteria for the presence of the maximal ideal in the set of associated primes
Mehrdad Nasernejad, Jonathan Toledo
In this paper, we establish some criteria to detect the presence of the maximal ideal in the set of associated primes of powers of monomial ideals in the polyn…
On the copersistence property and nearly copersistence property of monomial ideals
Mehrdad Nasernejad, Jonathan Toledo
In this paper we investigate the monomial ideals which satisfy the copersistence property or nearly copersistence property.
On the strong persistence property and normally torsion-freeness of square-free monomial ideals
Alain Bretto, Mehrdad Nasernejad, Jonathan Toledo
In this paper, we first show that any square-free monomial ideal in has the strong persistence property. Next we will provide a criterion for a minimal…
Normally torsion-freeness and normality criteria for monomial ideals
M. Nasernejad, V. Crispin Quinonez, J. Toledo
In this paper, we focus on the associated primes of powers of monomial ideals and asymptotic behavior properties such as normally torsion-freeness, normality, the strong persistenc…
On the normally torsion-freeness of square-free monomial ideals
Mehrdad Nasernejad, Veronica Crispin Quiñonez, Winfried Hochstättler
Let be a square-free monomial ideal, be a prime monomial ideal in , be a square-free monomial in with $\mathrm{supp}(h) \…
A classification of Mengerian -uniform hypergraphs derived from graphs
Winfried Hochstättler, Mehrdad Nasernejad
In this paper, we give a classification of all Mengerian -uniform hypergraphs derived from graphs.
The edge ideals of -spread -partite hypergraphs
Aslı Musapaşaoğlu, Mehrdad Nasernejad, Ayesha Asloob Qureshi
Inspired by the definition of -spread monomial ideals, in this paper, we introduce -spread -partite hypergraph and study its edge ideal $I(K^{\bf t…
Algebraic implications of neighborhood hypergraphs and their transversal hypergraphs
Mehrdad Nasernejad, Ayesha Asloob Qureshi
In this paper, we unfold balanced and totally balanced neighborhood hypergraphs to discover new classes of normally torsion-free monomial ideals. As a consequence, we establish tha…
Normality and associated primes of Closed neighborhood ideals and dominating ideals
Mehrdad Nasernejad, Somayeh Bandari, Leslie G. Roberts
In this paper, we first give some sufficient criteria for normality of monomial ideals. As applications, we show that closed neighborhood ideals of complete bipartite graphs are no…
Results on the normality of square-free monomial ideals and cover ideals under some graph operations
Ibrahim Al-Ayyoub, Mehrdad Nasernejad, Kazem Khashyarmanesh +2
In this paper, we introduce techniques for producing normal square-free monomial ideals from old such ideals. These techniques are then used to investigate the normality of cover i…
Dominating ideals and closed neighborhood ideals of graphs
Mehrdad Nasernejad, Ayesha Asloob Qureshi, Somayeh Bandari +1
We study the closed neighborhood ideals and the dominating ideals of graphs, in particular, of trees and cycles. We prove that the closed neighborhood ideals and the dominating ide…
On the embedded associated primes of monomial ideals
Mirsadegh Sayedsadeghi, Mehrdad Nasernejad, Ayesha Asloob Qureshi
Let be a square-free monomial ideal in a polynomial ring over a field , be the graded maximal ideal of , and $\{u…
Classes of normally and nearly normally torsion-free monomial ideals
Mehrdad Nasernejad, Ayesha Asloob Qureshi, Kazem Khashyarmanesh +1
In this paper, our main focus is to explore different classes of nearly normally torsion-free ideals. We first characterize all finite simple connected graphs with nearly normally…
On the matroidal path ideals
Mehrdad Nasernejad, Kazem Khashyarmanesh, Ayesha Asloob Qureshi
We prove that the set of all paths of a fixed length in a complete multipartite graph is the bases of a matroid. Moreover, we discuss the Cohen-Macaulayness and depth of powers of…