Let M be proper ideal of Boolean ring R. Which of the following is/are true? 1.$R/M$ is Boolean ring. 2.$R/M$ $\cong$ $Z_2$ if and only if M is maximal ideal.
2026-03-29 22:26:27.1774823187
Proper ideal of Boolean ring
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Hints:
1) $(x+M)(x+M)=$?
2) $R/M$ is certainly a field. An element of a field satisfying $a^2=a$ is a root of the polynomial $x^2-x$. With 1), what does this say about the field?