{"paper":{"title":"Poincar\\'e series of compressed local Artinian rings with odd top socle degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Adela Vraciu, Andrew R. Kustin, Liana M. Sega","submitted_at":"2016-07-19T14:19:09Z","abstract_excerpt":"We define a notion of compressed local Artinian ring that does not require the ring to contain a field. Let $(R,\\mathfrak m)$ be a compressed local Artinian ring with odd top socle degree $s$, at least five, and $\\operatorname{socle}(R)\\cap \\mathfrak m^{s-1}=\\mathfrak m^s$. We prove that the Poincar\\'e series of all finitely generated modules over $R$ are rational, sharing a common denominator, and that there is a Golod homomorphism from a complete intersection onto $R$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05594","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"}