19.49 (2018)

A skew brace is a set $B$ equipped with two operations $+$ and $\cdot$ such that $(B, +)$ is an additively written (but not necessarily abelian) group, $(B, \cdot)$ is a multiplicatively written group, and $a \cdot (b + c) = ab - a + ac$ for any $a, b, c \in B$.

Let $A$ be a skew brace with left-orderable multiplicative group. Is the additive group of $A$ left-orderable?