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.

Keywords:

• Normally torsion-free ideals
• nearly normally torsion-free ideals
• associated prime ideals
• t-spread monomial ideals
• hypergraphs

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 13B25
• 13F20
• 05E40

Acknowledgments

We would like to thank Professor Adam Van Tuyl for his valuable comments in preparation of Theorem 4.9. In addition, the authors are deeply grateful to the referee for careful reading of the manuscript and valuable suggestions which led to significant improvements in the quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).