Algebraic implications of neighborhood hypergraphs and their transversal hypergraphs

2022/08/30 by Mehrdad Nasernejad, Nasernejad, Mehrdad, Ayesha Asloob Qureshı +1 · 2 citations
Mathematics · #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2208.14040

openalex publication_date 2022/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 that the closed neighborhood ideals and the dominating ideals of strongly chordal graphs are normally torsion-free. We discuss the stable sets of associated primes of the dominating ideals of cycles and characterize all the cycles with normally torsion-free dominating ideals.

Cited by

• Demotions of ideals in commutative rings with applications to normally torsion-freeness
• Associated primes of the second power of closed neighborhood ideals of graphs

Related

• Dominating ideals and closed neighborhood ideals of graphs
• Normality and associated primes of Closed neighborhood ideals and dominating ideals
• Almost normally torsionfree ideals
• Normally torsion-freeness and normality criteria for monomial ideals
• Closed Neighborhood Ideals of Finite Simple Graphs