  We study some relations between left cancellative left semi-braces and other
existing algebraic structures. In particular, we show that every left
semi-brace arises from a left seminear-ring, extending the correspondence given
by Rump between skew left braces and left near-rings in \cite{rump2019set}.
Moreover, we show a correspondence between certain groups semidirect products
and left cancellative left semi-braces satisfying an additional hypothesis on
the set of idempotents. As an application, we classify left cancellative left
semi-braces of size $pq$ and $2p^2$ such that the set of idempotents $E$ is a
Sylow subgroup of the multiplicative group. Finally, we study various type of
nilpotency, recently introduced in \cite{catino2022nilpotency}, of these left
semi-braces.
