  A subsemigroup $S$ of an inverse semigroup $Q$ is a left I-order in $Q$ if
every element in $Q$ can be written as $a^{-1}b$ where $a,b \in S$ and $a^{-1}$
is the inverse of $a$ in the sense of inverse semigroup theory. If we insist on
$a$ and $b$ being $\mathcal{R}$-related in $Q$, then we say that $S$ is a
straight left I-order in $Q$. We give necessary and sufficient conditions for a
semigroup to be a left I-order in a bisimple inverse $\omega$-semigroup.
