ring homomorphism

A ring homomorphism is a function between two algebraic structures called rings that preserves their fundamental operations—addition and multiplication. It ensures that combining elements and their products in the first ring translate consistently into the second ring. Specifically, if you add or multiply two elements and then apply the function, it's the same as applying the function to each element first and then performing the operation in the second ring. This concept helps us understand how different algebraic systems relate to each other while maintaining their core properties, enabling consistent translations and comparisons across mathematical contexts.