2 problems

Let $K$ be a finite field, let $\varepsilon>0$ and $N\in\mathbb{N}$. For a metric group $(G,\|\cdot\|)$ with $\|\cdot\|\leq 1$, let $K[G]$ be its group ring, let $l(a)$ denote the…

Let $F$ be a field and $G$ a countable group. The group algebra $F(G)$ is directly finite, meaning that for any $x,y\in F(G)$, $xy=1$ implies $yx=1$. Direct finiteness conjecture.…