Fractional ideals are a generalization of ideals in the ring of integers of a number field, allowing for the inclusion of elements that may not be whole integers but can be expressed as fractions. They play a crucial role in the study of algebraic number theory, particularly within Dedekind domains, where every non-zero fractional ideal can be uniquely factored into prime fractional ideals, highlighting their relationship with the ideal class group and providing insights into the structure of these domains.
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