You are confusing the binary operations in the two setsAand End(A). The definition of + in End(A) is: , (f+g):A→Awhere (f+g)(a) = f(a)g(a) for alla∊A.

This may look strange, but that’s because you are writing product of elements inAmultiplicatively.

However, sinceAis an Abelian group, why not denote the binary operation inAadditively? To avoid confusion, let’s write for the operation in End(A) and + for the operation inA. So we have

for alla∊A.

Now that looks more intuitive. Hence, for any endomorphisms f and g and any :

Hence .