Higher conservation laws and algebraic Bethe Ansatze for the supersymmetric t-J model

We construct the enveloping fundamental spin model of the t-J Hamiltonian using the quantum-inverse-scattering method (QISM), and present all three possible algebraic Bethe Ansa$iuml-tze. Two of the solutions have been previously obtained in the framework of the coordinate-space Bethe Ansatz by Sutherland and by Schlottmann and Lai, whereas the third solution is new. The formulation of the model in terms of the QISM enables us to derive explicit expressions for higher conservation laws.