Derivations on the Module Extension Banach Algebras

We correct some results presented in [M. Eshaghi Gordji, F. Habibian, and A. Rejali, Int. J. Contemp. Math. Sci. , 2, No. 5, 213 (2007)]. By using the obtained consequences, we establish necessary and sufficient conditions for the module extension A ⨁ X to be ( I ⨁ Y )-weakly amenable, where I is a closed ideal of the Banach algebra A and Y is a closed A -submodule of the Banach A -bimodule X. We apply this result to the module extension A ⨁ ( X 1 u X 2 ) , where X 1 and X 2 are two Banach A -bimodules.