Boolean rings are commutative
Suppose
- Prove
for every element . - Show
must be commutative. Hint: Consider .
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Suppose $R$ is a ring such that $r^2=r$ for every element $r\in R$.
\begin{enumerate}[label=\alph*)]
\item Prove $r=-r$ for every element $r\in R$.
\item Show $R$ must be commutative. {\itshape Hint:} Consider $(a+b)^2$.
\end{enumerate}