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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?

  • 1
    There's a proof of this in the first chapter of Halmos' _Lectures on Boolean Algebras_.2011-09-08
  • 0
    This is exercise 15 from chapter 7 Introduction to Rings section 1 Definitions and Examples in Dummit and Foote, 3rd edition.2014-09-19

9 Answers 9