Algebraic number theory

Different ideal

In algebraic number theory, the different ideal (sometimes simply the different) is defined to measure the (possible) lack of duality in the ring of integers of an algebraic number field K, with respect to the field trace. It then encodes the ramification data for prime ideals of the ring of integers. It was introduced by Richard Dedekind in 1882. (Wikipedia).

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Related pages

Richard Dedekind | Hasse–Arf theorem | Algebraic number field | Prime ideal | Pontryagin duality | Discriminant of an algebraic number field | Local Fields | Ideal norm | Tower of fields | Finite extensions of local fields | Ramification (mathematics) | Local field | Field trace | Fractional ideal | Ring of integers | Algebraic number theory | Kähler differential | Simple extension