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The Extension Property in the Category of Direct Sum of Cyclic Torsion-Free Modules over a BFD[.]) proved that the automorphisms having the property of extension in the category of groups, characterize the inner automorphisms. Ben Yakoub (Port. Math. .(2):231–233, 1994, [.]) proved that this result is not true in the category of algebras. But there are some very important results in the cate