Let $R$ be a commutative ring with unity and let $B(R)$ be the set of all idempotent elements in $R$.
Show for $b\in B(R)$, the $R$-modules $R$ and $Rb \times R(1-b)$ are isomorphic to one another.
Let $R$ be a commutative ring with unity and let $B(R)$ be the set of all idempotent elements in $R$.
Show for $b\in B(R)$, the $R$-modules $R$ and $Rb \times R(1-b)$ are isomorphic to one another.