Kaplansky's zero divisor and unit conjectures on elements with supports of size $3$

Alireza Abdollahi, Zahra Taheri

Kaplansky's zero divisor conjecture (unit conjecture, respectively) states that for a torsion-free group $G$ and a field $\mathbb{F}$, the group ring $\mathbb{F}[G]$ has no zero di…