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 ⨁ (X1 u X2), where X1 and X2 are two Banach A-bimodules.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 4, pp. 566–576, April, 2021. Ukrainian DOI: 10.37863/umzh.v73i4.240.
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Teymouri, A., Bodaghi, A. & Bagha, D.E. Derivations on the Module Extension Banach Algebras. Ukr Math J 73, 661–673 (2021). https://doi.org/10.1007/s11253-021-01950-x
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DOI: https://doi.org/10.1007/s11253-021-01950-x