1. The problem statement, all variables and given/known data Let R and R' are rings and phi: R to R' is a ring homomorphism such that phi[R] is not identically 0'. Show that if R has unity 1 and R' has no 0 divisors, then phi(1) is a unity for R'. 2. Relevant equations 3. The attempt at a solution Its relatively obviously why phi(1) has to be unity for the subring phi[R]. I don't see why phi(1)r' has to be r' for every r' in R'.