Cyclotomic field

Kronecker’s root of unity lemma

If 𝛼 is a nonzero algebraic integer whose embeddings into ℂ all have absolute value at most 1, them 𝛼 is a root of unity.¹ alg

Proof

proof

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develop | en | SemBr

Footnotes

1. 2022. Algebraic number theory course notes, ¶2.35, p. 49 ↩