Abstarct: Let R be a finite ring with identity. T its set of idempotents. We study the subsets of T that can be closed under multiplication and the idempotents that fact has to the structure of R. We consider the subset M of all minimal idempotents and zero. We achieve this by studing the properties of units that are preserved by idempotents. We prove that M is closed under multiplication if and only if R is a direct sum of local rings.