(R,+) is an abelian group. so an endomorphism of (R,+) is just a group homomorphism:

so which means is closed under addition.b) Show that is a subring of

so which means is closed under multiplication.

if has an identity element then for all and and thus

for this part you do need to have define the map by then we also havec) Prove the analogue of Cayley's theorem for by showing that of (b) is isomorphic to

so is a ring homomorphism. to show that it's 1-1, let then for all put to get finally, it's trivial that is onto.