Bicyclic semigroups of left I-quotients
  In this article we study left I-orders in the bicyclic monoid $\mathcal{B}$. We give necessary and sufficient conditions for a subsemigroup of $\mathcal{B}$ to be a left I-oreder in $\mathcal{B}$. We then prove that any left I-order in $\mathcal{B}$ is straight. 
Nassraddin Ghroda
math.GR math.RA