Endomorphism Ring

Given an abelian group $A$, the ring produced by the set of endomorphisms of $A$ with addition of morphisms defined as $f + g \mapsto (x \mapsto f(x) + g(x))$ and multiplication of morphisms defined as $f \cdot g \mapsto (x \mapsto f(g(x)))$ is called the endomorphism ring of $A$. Additionally, it is denoted with $\text{End}A$.