Zero divisors of an endomorphism ring

  • #1
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Main Question or Discussion Point

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.
 

Answers and Replies

  • #2
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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?
 

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