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A group ring $R[G]$ is a ring constructed in a natural way from a ring $R$ and a group $G$.
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Description of the units of the group ring Fp[Fp] ?
You can use that $\mathbb{F}_p[\mathbb{Z}/p]\cong \mathbb{F}[\epsilon]/\epsilon^p,$ where $\epsilon=1-\sigma$ for $\sigma$ a generator of the group $\mathbb{Z}/p$. This is an Artin local ring, and fro …