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/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

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

Zendy Tools

Zendy Open

Let $k$ be a division ring and let $G$ be either a torsion-free virtuallycompact special group or a finitely generated torsion-free $3$-manifold group.We embed the group algebra $kG$ in a division ring and prove that the embeddingis Hughes-free whenever $G$ is locally indicable. In particular, we prove thatKaplansky's Zero Divisor Conjecture holds for all group algebras oftorsion-free $3$-manifold groups. The embedding is also used to confirm aconjecture of Kielak and Linton. Thanks to the work of Jaikin-Zapirain andLinton, another consequence of the embedding is that $kG$ is coherent whenever$G$ is a virtually compact special one-relator group.  If $G$ is a torsion-free one-relator group, let $\overline{kG}$ be thedivision ring containing $kG$ constructed by Lewin and Lewin. We prove that$\overline{kG}$ is Hughes-free whenever a Hughes-free $kG$-division ringexists. This is always the case when $k$ is of characteristic zero; in positivecharacteristic, our previous result implies that this happens when $G$ isvirtually compact special.

Division rings for group algebras of virtually compact special groups and $3$-manifold groups