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Lattices and hypergraphs associated to square-free monomial ideals
- Source :
- Communications in Algebra. 50:4710-4724
- Publication Year :
- 2022
- Publisher :
- Informa UK Limited, 2022.
-
Abstract
- Given a square-free monomial ideal $I$ in a polynomial ring $R$ over a field $\mathbb{K}$, one can associate it with its LCM-lattice and its hypergraph. In this short note, we establish the connection between the LCM-lattice and the hypergraph, and in doing so we provide a sufficient condition for removing higher dimension edges of the hypergraph without impacting the projective dimension of the square-free monomial ideal. We also offer algorithms to compute the projective dimension of a class of square-free monomial ideals built using the new result and previous results of Lin-Mantero.<br />The paper is split into two via the suggestion of the editor. The second part will be submitted soon
Details
- ISSN :
- 15324125 and 00927872
- Volume :
- 50
- Database :
- OpenAIRE
- Journal :
- Communications in Algebra
- Accession number :
- edsair.doi.dedup.....5bb5f39021886da194afa117aab2b1f2