English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We apply small cancellation methods originating from group theory toinvestigate 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 freegroup $\mathcal{F}$ over the field $\mathbb{Z}_2$, and the ideal $\mathcal{I}$is generated by a single trinomial $1 + v + vw$, where $v$ is a complicatedword 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 linearbasis of $\mathbb{Z}_2\mathcal{F} / \mathcal{I}$ (thus showing that$\mathbb{Z}_2\mathcal{F} / \mathcal{I}\neq 0$). This is the first step inconstructing rings with exotic properties.

Construction of a quotient ring of $\mathbb{Z}_2\mathcal{F}$ in which a binomial $1 + w$ is invertible using small cancellation methods