{"paper":{"title":"Tangent Cone of Numerical Semigroup Rings of Embedding Dimension Three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Yi-Huang Shen","submitted_at":"2008-08-15T16:33:53Z","abstract_excerpt":"In this paper, we give new characterizations of the Buchsbaum and Cohen-Macaulay properties of the tangent cone $\\gr_\\frakm(R)$, where $(R,\\frakm)$ is a numerical semigroup ring of embedding dimension 3. In particular, we confirm the conjectures raised by Sapko on the Buchsbaumness of $\\gr_\\frakm(R)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.2162","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}