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## Homework Statement

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'.

## Homework Equations

## 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'.

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