SOLVED: Consider the following diagram of homomorphisms of modules over R:A -> B -> CA' -> B' -> C'where the rows are exact and the squares are commutative. Show that f and g define a sequence Ker(a) -> Ker(b) -> Ker(c) and f' and g' induce a sequence Coker(a) -> Coker(b) -> Coker(c). Prove that the sequence is exact if f' -> B' is a monomorphism and that the sequence is exact if g: B -> C is an epimorphism.

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Abelian Group, Ring, Left R-Module, Right R-Module, R-Module, Bi-Module, Factor Module, R-homomorphism, Examples of R-homomorphism are described here | Masum Math Solution