Ring morphism

Let \(R\) and \(S\) be rings. A ring morphism is a map \(f\colon R\to S\) such that for all \(a, b\in R\):

• \(f(1_R) = 1_S\);

• \(f(a+b) = f(a) + f(b)\);

• \(f(ab) = f(a)f(b)\).