Suppose that R is a ring and that a2 = a for all a in R.

Chapter 12, Problem 50E

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Suppose that R is a ring and that \(a^2 = a\) for all a in R. Show that R is commutative. [A ring in which \(a^2 = a\) for all a is called a Boolean ring, in honor of the English mathematician George Boole (1815–1864).]

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