In algebraic number theory, 'split' refers to the behavior of a prime ideal in the ring of integers of a number field when it factors into distinct prime ideals in an extension of that field. When a prime ideal splits, it can be represented as a product of prime ideals, indicating that the ideal can be completely factored in the larger ring. This behavior is crucial for understanding how primes behave in different number fields and is closely tied to concepts such as ramification and inertia.
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