This question already has an answer here:
- In a ring $a*a=0$ then $a+a=0$ 3 answers
I am stuck in a question for Algebraic Structures:
I need to prove the following:
Let $R$ be a ring. If $a^2=a$ for any $a\in R$, then $a+a=0$ for any $a\in R$.
(of course $+$, $\cdot$ and $0$ regarding $R$)
P.S. This is similar to a different question I asked (if $a \cdot a = 0$ then $a + a = 0$) but I wasn't able to apply the ideas from there. In that question we assumed that $R$ is a unity ring.