## Ring homomorphisms map an identity element to an identity or a zero divisor

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.17 Solution: (1) Suppose $\varphi(1_R) = r$, with $r \neq 1$. First, if $r = 0$, then…

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.17 Solution: (1) Suppose $\varphi(1_R) = r$, with $r \neq 1$. First, if $r = 0$, then…