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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.13617 |
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Table of Contents:
- In this article, we investigate the combinatorial and algebraic properties of the lcm-lattice associated with the edge ideal of a hypergraph. Let $\H$ be a hypergraph, $I(\H)$ its corresponding edge ideal in a polynomial ring in $n$ variables, and $\mathrm{Icm}(I(\H))$ the associated lcm-lattice. We establish conditions under which the lcm-lattice of an edge ideal is Boolean, modular, or complemented. Furthermore, we extend these results to the case of the product of lcm-lattices in the complemented case. Additionally, we study the effects of polarization on the lcm-lattices of $I(\H)$ and its polarized ideal.