Question 27
Let $(R, +, \cdot)$ be a unit ring such that for all $x \in R$ one can find $e_1, e_2 \in R$, such that $e_1^2 = e_1$, $e_2^2 = e_2$ and $x = e_1e_2$. Show that:
a) $1$ is the only invertible element in $R$;
b) $x^2 = x$, for all $x \in R$.
a) $1$ is the only invertible element in $R$;
b) $x^2 = x$, for all $x \in R$.