Let R be a ring. Show that an R-module M is isomorphic to direct sum of A1 and A2 if and only if there are R-homomorphisms f_i: A_i---->M, for i=1,2, such that for any module B and R-homomorphisms g_i:A_i----->B, for i=1,2, there is unique R-homomorphism h:M--->B so that g_i=h(f)

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