Exact Sequences in Abelian Groups

This lecture introduces the fundamental notion of an exact sequence of homomorphisms between abelian groups, presenting examples including the exact sequence associated with a direct sum of abelian groups. It also explores a class of more structured exact sequences known as 'split'. The lecture covers the definition of a short exact sequence in abelian groups, the concept of injective sequences, and the conditions for a sequence to be split. Various examples and proofs are provided to illustrate these concepts.