{"paper":{"title":"Quotients of even rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Dylan Wilson, Jeremy Hahn","submitted_at":"2018-09-13T00:53:20Z","abstract_excerpt":"We prove that if $R$ is an $\\mathbb{E}_2$-ring with homotopy concentrated in even degrees, and $\\{x_j\\}$ is any sequence of elements in $\\pi_{2*}(R)$, then $R/(x_1,x_2,\\cdots)$ admits the structure of an $\\mathbb{E}_1$-$R$-algebra. This removes an assumption, common in the literature, that $\\{x_j\\}$ be a regular sequence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.04723","kind":"arxiv","version":1},"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"}