Definition:Canonical Epimorphism

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Definition

Let $m \in \Z$.

Let $f:\Z \to \Z_m$ be a mapping such that:

$\forall n \in \Z: f(n) = \left[\!\left[{n}\right]\!\right]_m$

where:

$\Z_m$ denotes the integers modulo $m$.
$\left[\!\left[{n}\right]\!\right]_m$ denotes the residue class of $n$ modulo $m$.

Then $f$ is referred to as the canonical epimorphism ( from $\Z$ to $\Z_m$).


That this is an epimorphism is proved in Canonical Epimorphism is Epimorphism.


Sources