If you find any mistakes, please make a comment! Thank you.

Every nonzero Boolean ring has characteristic 2

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.27

Solution: Let $R$ be a Boolean ring. Note that $$1+1 = (1+1)^2 = 1+1+1+1,$$ so that $1+1 = 0$. Thus the characteristic of $R$ is at most 2. Since $R$ is nontrivial, we have $1 \neq 0$. Thus the characteristic of $R$ is exactly 2.


This website is supposed to help you study Linear Algebras. Please only read these solutions after thinking about the problems carefully. Do not just copy these solutions.
Close Menu