Definition:Character (Number Theory)

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Definition

Let $\struct {G, +}$ be a finite abelian group.

Let $\struct {\C_{\ne 0}, \times}$ be the multiplicative group of complex numbers.


A character of $G$ is a group homomorphism:

$\chi: G \to \C_{\ne 0}$


Also see

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

This generalizes the number theorist's definition above.