Character ring

Definition

Definition with symbols

Given a group $G$, a field $k$, and a subring $R$ of $k$, the character ring of $G$ with respect to $k$ and $R$, is the ring of $R$-linear combinations of characters of representations of $G$ over $k$.

If $R$ is not specified, we assume it to be the smallest subring (viz the subring generated by 1, which is either $\mathbb {Z}$ or a prime field of the same characteristic as the whole field).