1. The problem statement, all variables and given/known data Let T:R-> S be a homomorphism of rings. Show that T(0_r) = 0_s. 2. Relevant equations 3. The attempt at a solution First off, the terminology used is kinda confusing. I take 0_r to be the zero in R. Is this correct? For some reason I recall my teacher quickly saying that it was the additive inverse or something. Perhaps I heard wrong, as that makes no sense. The way I am going about this is the following: Since T:R->S we take the 0 in r and map it to S. I mean, is there much more to say? By the definition of homomorphisms, we are mapping a 0 in R to S. If we mapped (1-1) (assuming 1 is in R) to S it would be still be 0.