Classes of normally and nearly normally torsion-free monomial ideals

TL;DR

This paper investigates classes of monomial ideals that are nearly normally torsion-free, providing characterizations for specific graph and hypergraph classes, advancing understanding of their algebraic and combinatorial properties.

Contribution

It characterizes all finite simple connected graphs with nearly normally torsion-free cover ideals and describes normally torsion-free t-spread principal Borel ideals as edge ideals of hypergraphs.

Findings

Characterization of graphs with nearly normally torsion-free cover ideals

Description of normally torsion-free t-spread principal Borel ideals

Connection between algebraic properties and hypergraph structures

Abstract

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 torsion-free cover ideals. Next, we characterize all normally torsion-free $t$-spread principal Borel ideals that can also be viewed as edge ideals of uniform multipartite hypergraphs.