Zero divisors with small supports in group algebras of torsion-free groups over a field
For any field $\mathbb{F}$ and all torison-free group $\mathbb{G}$, we prove that if $ab = 0$ for some non-zero $a, b \in \mathbb{F}[\mathbb{G}]$ such that $|supp(a)|$ $= 3$ and $a = 1 + α_{1}g_{1} + α_{2}g_{2}$, then $g_{1}, g_{2}$ satisfies certain relations in $\mathbb{G}$.
math.GR↗