{"paper":{"title":"Construction of a quotient ring of $\\mathbb{Z}_2\\mathcal{F}$ in which a binomial $1 + w$ is invertible using small cancellation methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"A. Atkarskaya, A. Kanel-Belov, E. Plotkin, E. Rips","submitted_at":"2018-07-26T11:27:31Z","abstract_excerpt":"We apply small cancellation methods originating from group theory to investigate the structure of a quotient ring $\\mathbb{Z}_2\\mathcal{F} / \\mathcal{I}$, where $\\mathbb{Z}_2\\mathcal{F}$ is the group algebra of the free group $\\mathcal{F}$ over the field $\\mathbb{Z}_2$, and the ideal $\\mathcal{I}$ is generated by a single trinomial $1 + v + vw$, where $v$ is a complicated word depending on $w$. In $\\mathbb{Z}_2\\mathcal{F} / \\mathcal{I}$ we have $(1 + w)^{-1} = v$, so $1 + w$ becomes invertible. We construct an explicit linear basis of $\\mathbb{Z}_2\\mathcal{F} / \\mathcal{I}$ (thus showing that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10070","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"}