nLab integers modulo n



Given a natural number nn, the ring of integers modulo nn is the quotient ring /n\mathbb{Z}/n\mathbb{Z}.

These are also the quotient rig /n\mathbb{N}/n\mathbb{N}.


The integers modulo nn are precisely the finite cyclic rings, since the underlying set is the finite set of cardinality nn and the underlying abelian group is the cyclic group of order nn.

Given any positive integer nn, /n\mathbb{Z}/n\mathbb{Z} is a prefield ring whose monoid of cancellative elements consists of all integers mm modulo nn which are coprime with nn. For nn a prime number this is a prime field, and for nn a prime power this is a prime power local ring.

See also


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.