All Questions

$\newcommand{\End}{\operatorname{End}}$ let $R$ be a local ring, $\varphi\in \End(R_{R}^{2})$, $\overline{\varphi}\in \End(\overline{R}_{\overline{R}}^{2})$, $\overline{R} =R/J(R)$ , $J(R)$= ...

Let $R$ be a finite local $\mathbb{F}_q$-algebra. Assume that $R\cong R^*$ as left $R$-modules. Are there any known results about the abelianization $(R^{\times})_{\mathrm{ab}}$? (We can factor $R$ be ...