Classes of normally and nearly normally torsion-free monomial ideals

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.