A ring homomorphism is a function between two rings that preserves the ring operations, specifically addition and multiplication. This means that if you have two rings, R and S, a ring homomorphism f from R to S satisfies f(a + b) = f(a) + f(b) and f(ab) = f(a)f(b) for all elements a and b in R, while also preserving the multiplicative identity if one exists. This concept is crucial in understanding how different algebraic structures interact with each other.
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