{"paper":{"title":"Conditions for the Yoneda algebra of a local ring to be generated in low degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Justin Hoffmeier, Liana M. \\c{S}ega","submitted_at":"2014-03-27T22:52:51Z","abstract_excerpt":"The powers ${\\mathfrak m}^n$ of the maximal ideal $\\mathfrak m$ of a local Noetherian ring $R$ are known to satisfy certain homological properties for large values of $n$. For example, the homomorphism $R\\to R/{\\mathfrak m}^n$ is Golod for $n\\gg 0$. We study when such properties hold for small values of $n$, and we make connections with the structure of the Yoneda Ext algebra, and more precisely with the property that the Yoneda algebra of $R$ is generated in degrees $1$ and $2$. A complete treatment of these properties is pursued in the case of compressed Gorenstein local rings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7240","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"}