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Infinite Boolean rings exist


Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.22

Give an example of an infinite boolean ring.


Solution: If $X$ is an infinite set, then $\mathcal{P}(X)$ is infinite. We saw in Exercise 7.1.21 that $\mathcal{P}(X)$ is a Boolean ring under symmetric difference and intersection.


Linearity

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