Definition:Character (Number Theory)

Definition
Let $G$ be a finite abelian group.

A character of $G$ is a group homomorphism:


 * $\chi : G \to \C^\times$

where $\C^\times$ is the multiplicative Group of Units of $\C$, Group of Complex Units.

Also see
In algebra, character refers to the trace of a representation of $G$.

This generalizes the number theorist's definition above.