  We extend the rack algebra Z[X] defined by Andruskiewitsch and Grana to the
case of biracks, enabling a notion of birack modules. We use these birack
modules to define an enhancement of the birack counting invariant generalizing
the birack module counting invariant in [8]. We provide examples demonstrating
that the enhanced invariant is not determined by the Jones or Alexander
polynomials and is strictly stronger than the unenhanced birack counting
invariant.
