Description
Let A be an abelian group and f and g be two group homomorphisms from A into itself. Then the functions may be added pointwise to produce a group homomorphism. Under this operation End(A) is an Abelian group. With the additional operation of function composition, End(A) is a ring with multiplicative identity. The multiplicative identity is the identity function on A.
If the set A does not form an Abelian group, then the above construction does not result in the set of endomorphisms being an additive group, as the sum of two homomorphisms need not be a homomorphism in that case. This set of endomorphisms is a canonical example of a near-ring which is not a ring.
Read more about this topic: Endomorphism Ring
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