Kindly help me in this one.
Is Z/2Z always a subring of any non-zero Boolean ring with identity?
I think it is not true always. Let X be a non-empty set. P(X) be the set of all subsets of X. Then P(X) is a Boolean ring with the binary operations symmetric difference and intersection of sets. Z/2Z is not subset of any non-empty set X, also the binary operations are different. But I am not sure about my answer.