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$\newcommand{\End}{\operatorname{End}}$

let $R$ be a local ring, $\varphi\in \End(R_{R}^{2})$, $\overline{\varphi}\in \End(\overline{R}_{\overline{R}}^{2})$, $\overline{R} =\frac{R}{J(R)}$ , $J(R)$= Jacobson radical $R$. where neither $\varphi$ nor $1-\varphi$ is invertible. why neither $\overline{\varphi}$ nor 1- $\overline{\varphi}$ is invertible in $End(\overline{R}_{\overline{R}}^{2})$ ?

$\newcommand{\End}{\operatorname{End}}$

let $R$ be a local ring, $\varphi\in \End(R_{R}^{2})$, $\overline{\varphi}\in \End(\overline{R}_{\overline{R}}^{2})$, $\overline{R} =R/J(R)$ , $J(R)$= Jacobson radical $R$. where neither $\varphi$ nor $1-\varphi$ is invertible. Why neither $\overline{\varphi}$ nor 1- $\overline{\varphi}$ is invertible in $\End(\overline{R}_{\overline{R}}^{2})$ ?

let R be a local ring, $\varphi$ $\in$ $End(R_{R}^{2})$, $\overline{\varphi}$ $\in$ $End($\overline{R}$_{\overline{R}}^{2})$ , $\overline{R}$ $=\frac{R}{J(R)}$ , J(R)= Jacobson radical R. where neither $\varphi$ nor $1-\varphi$ is invertible. why neither $\overline{\varphi}$ nor 1- $\overline{\varphi}$ is invertible in $End($\overline{R}$_{\overline{R}}^{2})$ ?

$\newcommand{\End}{\operatorname{End}}$

let $R$ be a local ring, $\varphi\in \End(R_{R}^{2})$, $\overline{\varphi}\in \End(\overline{R}_{\overline{R}}^{2})$, $\overline{R} =\frac{R}{J(R)}$ , $J(R)$= Jacobson radical $R$. where neither $\varphi$ nor $1-\varphi$ is invertible. why neither $\overline{\varphi}$ nor 1- $\overline{\varphi}$ is invertible in $End(\overline{R}_{\overline{R}}^{2})$ ?