Algebraic number theory MOC

Logarithmic embedding

Let be a number field with signature with real embeddings and representative unreal embeddings . The Logarithmic embedding is a group homomorphism defined by #m/def/num/alg

We call the unit lattice for , and its covolume is called the regulator.

Properties

1. The norm of an element is related to the sum of its image by

where is the summation map. 2. , the group of roots of unity, by Kronecker's root of unity lemma.

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