Group ring
= Group ring
{title2=$R[G]$}
{wiki}
The <group ring> $R[G]$ consists of finite formal sums $\sum_{g\in G}r_gg$ with coefficients in a <ring> $R$. Addition is coefficientwise and multiplication extends the <group operation> and multiplication in $R$ distributively. A <group algebra> is the case in which $R$ is a <field>.