Ideal classes are equivalence classes of fractional ideals in the context of algebraic number theory, particularly related to the arithmetic of number fields. They provide a way to measure the failure of unique factorization in rings of integers of number fields, where each ideal class represents a distinct way that ideals can behave with respect to divisibility and multiplication. Understanding ideal classes is crucial for applications in number theory, such as computing class numbers and studying properties of algebraic integers.
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