I need to prove that zero is one at the trivial ring, but I don't have yet that one is a member of the trivial ring (the only constant at my zero ring is zero). So I thought to prove first that, if R is a ring with one (now I have the constant one inside the ring), then if the trivial ring has an identity, it must be the one (since the trivial ring is an R subring). After that I would prove that zero is an identify. I'm in trouble at the first step, that is, to show that one is trivial ring member. Could someone help me?
Edit $ $ In my definition a ring doesn't necessarily have a multiplicative identity "one".