Mohammed Rafiq Namiq

activity

20222026

most citedThe graded Betti numbers of truncation of ideals in polynomial rings

1 citations · 1 across the 10 of their papers we have counts for

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math.AC2026

Regularity of Symbolic Powers of Co-Chordal Edge Ideals

Chwas Ahmed, Mohammed Rafiq Namiq

Let $G$ be a finite simple co-chordal graph with at least one edge, and let $I (G)$ be its edge ideal. Over an arbitrary field, we prove that the symbolic powers of $I (G)$ satisfy $…

math.AC2026

Betti Numbers of Sequentially Cohen-Macaulay Co-Chordal Graphs and Their Applications

Mohammed Rafiq Namiq

We study edge ideals of sequentially Cohen-Macaulay co-chordal graphs through the maximal-clique structure of their chordal complements. After making the required construction orde…

math.AC2026

Explicit Betti Numbers for Skeletons of Chordal Clique Complexes and Their Alexander Duals

Mohammed Rafiq Namiq

Let $Δ_{r} = Δ_{r} (n_{1}, \dots, n_{e})$ be the clique complex of a chordal graph with maximal cliques $S_{1}, \dots, S_{e}$ in a leaf order, where $n_{m} = ∣ S_{m} ∣$ , $r_m=|S_{m+1}\c…

math.AC2026

Vertex Dismissibility and Scalability of Simplicial Complexe

Mohammed Rafiq Namiq

We study three nonpure extensions of vertex decomposability, shellability, and Cohen-Macaulayness at the minimum facet dimension. For $b = indim Δ$ , strong vertex dismi…

math.AC2025

Initially Cohen-Macaulay Modules

Mohammed Rafiq Namiq

In this paper, we introduce initially Cohen-Macaulay modules over a commutative Noetherian local ring $R$ , a new class of $R$ -modules that generalizes both Cohen-Macaulay and seque…

math.AC2025

The Graded Betti Numbers of the Skeletons of Simplicial Complexes

Mohammed Rafiq Namiq

In this paper, we study a class $C$ of squarefree monomial ideals $I \subseteq R = K [x_{1}, \dots, x_{n}]$ over a field $K$ , defined by the condition that $\dim…

math.AC2022★ 1 cited

The graded Betti numbers of truncation of ideals in polynomial rings

Chwas Ahmed, Ralf Fröberg, Mohammed Rafiq Namiq

Let $R = K [x_{1}, \dots, x_{n}]$ , a graded algebra $S = R / I$ satisfies $N_{k, p}$ if $I$ is generated in degree $k$ , and the graded minimal resolution is linear the first $p$ steps,…

math.AC2022

Quasi-forest simplicial complexes and almost Cohen-Macaulay

Chwas Ahmed, Amir Mafi, Mohammed Rafiq Namiq

In this paper we study the quasi-forest simplicial complexes and we define the concept of simplicial $k$ -cycle (denoted by $S_{k}$ ) and simplicial $k$ -point (denoted by $\m…

math.AC2022

Sequentially Cohen-Macaulay Co-Chordal Graphs: Structure and Projective Dimension

Chwas Ahmed, Amir Mafi, Mohammed Rafiq Namiq

We introduce a class of chordal graphs called ( $d_{1}$ , $d_{2}$ , $\dots$ , $d_{q}$ )-trees. A graph belongs to this class if and only if its clique complex is sequentially Cohen-Macaulay, pro…