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Number Field Order


Let K be a number field of extension degree d over Q. Then an order O of K is a subring of the ring of integers of K with d generators over Z, including 1.

The ring of integers of every number field K is an order, known as the maximal order, of K. Every order of K is contained in the maximal order. If alpha is an algebraic integer in K, then Z[alpha] is an order of K, though it may not be maximal if d is greater than 2.


See also

Algebraic Integer, Extension Field Degree, Field Order, Number Field, Order, Ring, Ring of Integers

This entry contributed by David Terr

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Cite this as:

Terr, David. "Number Field Order." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/NumberFieldOrder.html

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