Hello all. How can I show that the center of a ring Z(R) is an ideal of a ring R iff R is commutative?
Thanks!
Well, the center is every element in the ring that commutes with the whole ring. So if the whole ring is commutative, the center will be the whole ring. So Z(R)=R, so Z(R) is an ideal....the other way of the if and only if proof is what I have been struggling with...