Solution Found!
Suppose that : R S is a ring homomorphism and that the
Chapter 15, Problem 64E(choose chapter or problem)
Suppose that \(\phi\): \(R\) \(\rightarrow\) \(S\) is a ring homomorphism and that the image of \(\phi\) is not {\(0\)}. If \(R\) has a unity and \(S\) is an integral domain, show that \(\phi\) carries the unity of \(R\) to the unity of \(S\). Give an example to show that the preceding statement need not be true if \(S\) is not an integral domain.
Questions & Answers
QUESTION:
Suppose that \(\phi\): \(R\) \(\rightarrow\) \(S\) is a ring homomorphism and that the image of \(\phi\) is not {\(0\)}. If \(R\) has a unity and \(S\) is an integral domain, show that \(\phi\) carries the unity of \(R\) to the unity of \(S\). Give an example to show that the preceding statement need not be true if \(S\) is not an integral domain.
ANSWER:
Step 1 of 2
Let be a ring with unity, an integral domain and is a non trivial homomorphism.