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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2605.13617 |
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| _version_ | 1866918499724558336 |
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| author | Mansha, Muneeba Ahmad, Sarfraz |
| author_facet | Mansha, Muneeba Ahmad, Sarfraz |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13617 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Some Properties of LCM-Lattices of Edge Ideals of k-Uniform Hypergraphs Mansha, Muneeba Ahmad, Sarfraz Commutative Algebra 06A06, 06A07, 06A11 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. |
| title | On Some Properties of LCM-Lattices of Edge Ideals of k-Uniform Hypergraphs |
| topic | Commutative Algebra 06A06, 06A07, 06A11 |
| url | https://arxiv.org/abs/2605.13617 |