What are the ideals of $End(R)$?

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Let $R$ be a ring (with unity if necessary) , then $End(R)$ i.e. the set of endomorphism of the ring $R$ (the set of all ring homomorphisms from $R$ to $R$ ) forms a ring under point-wise function addition and function composition . What are the ideals of this ring $End(R)$ ? If we replace $R$ by any commutative group $G$ , then also $End(G)$ is a ring under function addition and composition ; what then are the ideals of $End(G)$ ?