transfinite arithmetic, cardinal arithmetic, ordinal arithmetic
prime field, p-adic integer, p-adic rational number, p-adic complex number
arithmetic geometry, function field analogy
Given a natural number $n$, the ring of integers modulo $n$ is the quotient ring $\mathbb{Z}/n\mathbb{Z}$.
These are also the quotient rig $\mathbb{N}/n\mathbb{N}$.
The integers modulo $n$ are precisely the finite cyclic rings, since the underlying set is the finite set of cardinality $n$ and the underlying abelian group is the cyclic group of order $n$.
Given any positive integer $n$, $\mathbb{Z}/n\mathbb{Z}$ is a prefield ring whose monoid of cancellative elements consists of all integers $m$ modulo $n$ which are coprime with $n$. For $n$ a prime number this is a prime field, and for $n$ a prime power this is a prime power local ring.
e.g. example 5 in these notes: pdf
Last revised on January 22, 2023 at 21:28:17. See the history of this page for a list of all contributions to it.