Let A be a ring and b be an ideal of A. The quotient ring of A by b, denoted A/b is the ring of all equivalence classes A + b.
Prove that the assignment $$c → c/b$$ induces a one-to-one correspondence between the ideals of A that contain b and the ideals of A/b.
I am completely at a loss. I understand one-to-one to mean bijective so I assume it is necessary to show the mapping is both injective and surjective? I also don't know what c is supposed to be - is it an element of A? Please help!
