R is a ring and consider commutative diagram of R -modules with exact rows.
then I want to show that Gamma is isomorphism if and only if
here + is direct sum and teh first homomorphism sends a to \alpha(a),k_1(a)
and the second homomorphism sends (a_2,b) to k_2(a_2)-\beta(b)
here k_1 is homomorphism from A_1 to B_1 and k_2 is homomorphism from
A_2 to B_2.