## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### On the ring of integers of real cyclotomic fields

#### Abstract

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

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 92, Number 6 (2016), 73-76.

Dates
First available in Project Euclid: 1 June 2016

https://projecteuclid.org/euclid.pja/1464786481

Digital Object Identifier
doi:10.3792/pjaa.92.73

Mathematical Reviews number (MathSciNet)
MR3508577

Zentralblatt MATH identifier
1345.11073

Subjects
Primary: 11E09
Secondary: 11R18: Cyclotomic extensions

#### Citation

Yamagata, Koji; Yamagishi, Masakazu. On the ring of integers of real cyclotomic fields. Proc. Japan Acad. Ser. A Math. Sci. 92 (2016), no. 6, 73--76. doi:10.3792/pjaa.92.73. https://projecteuclid.org/euclid.pja/1464786481

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