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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.

Definition, Relative different & Ramification

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Definition

Relative different

Ramification

Local computation

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Different ideal

Nodes36
Edges35
Triples6
Avg. degree1.94
Density0.055556
Components1

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Different ideal

Top relations

related to Definition · 6
Different ideal → By, Dedekind's, Define, If OK, Its, OK

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Important terminology

different relative ideal ramification integers discriminant isbn fields δl algebraic number theory defined field ring springer-verlag zbl ok extension prime

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Different idealrelated to DefinitionIf OK0.60section
Different idealrelated to DefinitionOK0.60section
Different idealrelated to DefinitionIts0.60section
Different idealrelated to DefinitionDefine0.60section
Different idealrelated to DefinitionDedekind's0.60section
Different idealrelated to DefinitionBy0.60section

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