(2) Let R be a commutative ring with identity. An element e € R is called an idempotent if e² = e. (a) Suppose e, f are idempotents. Show that ef and e + f - ef are also idempotents. (b) The following is a remark of the question: Let S be the set of all idempotents in R. For e, f e S, define e V f = e + f - ef and e^ f = ef. Then (S, V, ^) form a Boolean ring. Suppose ef = e, show that the principle ideal eRC fR.

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