If X is an infinite set, then the family of all finite subsets of X forms a subring of the Boolean Ring .
The book says this statement is true, and we have to prove it... but i think it is false
i think the unity is X, and it is NOT finite, and it is an ideal????
well, it depends on how you define a subring: generally a subring doesn't have to have a multiplicative identity but if it has, then it should be equal to the identity element of the ring.
in your example, your subring doesn't have the identity element and that is fine.