Let be a commutative diagram of R-modules and R-module homomorphisms, with exact rows. Prove that: (a)

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Let image


be a commutative diagram of R-modules and R-module homomorphisms, with exact rows. Prove that:


(a) α1 an epimorphism and α2monomorphisms => α3 is a monomorphism;


(b) α5 a monomorphism and α24 epimorphisms => α3 is an epimorphism. 

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