Title: On the virtual singular braid monoid,
Abstract: We study the algebraic structures of the virtual singular braid monoid,
$VSB_n$, and the virtual singular pure braid monoid, $VSP_n$. The monoid
$VSB_n$ is the splittable extension of $VSP_n$ by the symmetric group $S_n$. We
also construct a representation of $VSB_n$.