Zero divisors of an endomorphism ring

[Danijel]

Let (A,+) be an Abelian group. Consider the ring E=End(A,A) of endomorphisms on the set A, with binary operations +, and *, where (f+g)(x)=f(x) + g(x), and (f*g)=f∘g.
I have tried to find zero divisors in this ring, but I just couldn't come up with an example.

 

[fresh_42]

Let (A,+) be an Abelian group. Consider the ring E=End(A,A) of endomorphisms on the set A, with binary operations +, and *, where (f+g)(x)=f(x) + g(x), and (f*g)=f∘g.
I have tried to find zero divisors in this ring, but I just couldn't come up with an example.

Have you heard about nilpotent endomorphisms / matrices?