Lattices and hypergraphs associated to square-free monomial ideals

Given a square-free monomial ideal $I$ in polynomial ring $R$ over field $\mathbb{K}$, one can associate it with its LCM-lattice and hypergraph. In this short note, we establish the connection between hypergraph, doing so provide sufficient condition for removing higher dimension edges of hypergraph without impacting projective ideal. We also offer algorithms to compute class ideals built using new result previous results Lin-Mantero.