A ring $R$ is a Boolean ring provided that $a^2=a$ for every $a \in R$. How can we show that every Boolean ring is commutative?
How to show that every Boolean ring is commutative?
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abstract-algebra
ring-theory
idempotents
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1There's a proof of this in the first chapter of Halmos' _Lectures on Boolean Algebras_. – 2011-09-08
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0This is exercise 15 from chapter 7 Introduction to Rings section 1 Definitions and Examples in Dummit and Foote, 3rd edition. – 2014-09-19