On the ring of integers of real cyclotomic fields. (English) Zbl 1345.11073

Yamagata, Koji; Yamagishi, Masakazu

Proc. Japan Acad., Ser. A 92, No. 6, 73-76 (2016).

Summary: Let \(\zeta_n\) be a primitive \(n\)th root of unity. As is well known, \(\mathbb Z[\zeta_n+\zeta_n^{-1}]\) is the ring of integers of \(\mathbb Q (\zeta_ n+\zeta_n^{-1})\). We give an alternative proof of this fact by using the resultants of modified cyclotomic polynomials.

MSC:

11R04	Algebraic numbers; rings of algebraic integers
11R18	Cyclotomic extensions

Keywords:

cyclotomic field; ring of integers; Chebyshev polynomials

References:

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