Algebraic Number Theory
A ring homomorphism is a structure-preserving map between two rings that respects the operations of addition and multiplication. This means that if you have two rings, say R and S, a function f from R to S is a ring homomorphism if it satisfies f(a + b) = f(a) + f(b) and f(ab) = f(a)f(b) for all elements a, b in R, and it also preserves the multiplicative identity if R has one. This concept plays a crucial role in understanding how algebraic integers relate to their minimal polynomials and how different rings interact with one another.
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