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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. 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