Definition:Canonical Epimorphism
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Definition
Let $m \in \Z$.
Let $f:\Z \to \Z_m$ be a mapping such that:
- $\forall n \in \Z: \map f n = \eqclass n m$
where:
- $\Z_m$ denotes the integers modulo $m$.
- $\eqclass n m$ 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
- 1974: Thomas W. Hungerford: Algebra ... (previous) ... (next): $\S 1.2$