I am having query in this MCQ. Let $R$ be a ring such that every element is idempotent then
(a) Every prime ideal is maximal ideal.
(b) Every maximal ideal is prime ideal
(c) if $|R|> 2$ implies $R$ never ID
(d) If $|R| > 2$ implies $R$ never field.
As every element is idempotent, they are taking about Boolean ring. And in Boolean ring every prime ideal is maximal and every maximal is prime hence option a and b is true. How to deal with option c and d. Actually both c and d are also given true. Can u explain or hint me why both has to be true. Just hint me, why for $|R|> 2$ is not Integral domain.
Thanks in advance!!