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 $\C$.

Note
In algebra, character refers to the trace of a representation of $G$. This generalizes the number theorist's definition above.