transfinite arithmetic, cardinal arithmetic, ordinal arithmetic
prime field, p-adic integer, p-adic rational number, p-adic complex number
arithmetic geometry, function field analogy
For $\zeta_n$ an $n$th root of unity and $k$ a field, consider the cyclotomic field $k(\zeta_n)$. The ring of integers of this field is called the ring of cyclotomic integers.
For $\mathbb{Q}$ the rational numbers, consider the cyclotomic field $\mathbb{Q}(\zeta_n)$. The ring of integers of this field is $\mathbb{Z}[\zeta_n]$, i.e. polynomials in $\zeta_n$ with integer coefficients.
See also
Created on October 7, 2018 at 08:45:47. See the history of this page for a list of all contributions to it.