Closability of Module −Derivatoins

Let  be a linear mapping from a dense subalgebra A of a Banach algebra B into B. In this note, we study the closability of a module ? derivation  from A into a B? bimodule M. Applying the notions of torsion-free modules and essential ideals, we present several results concerning the closability of such derivations. Also we investigate the closability of module ? derivations of the C? algebra B into a Hilbert B? bimodule M.