A unital ring is called clean (resp. strongly clean) if every element can be written
as the sum of an invertible element and an idempotent (resp. an invertible element
and an idempotent that commutes). T.Y. Lam proposed a question: which von
Neumann algebras are clean as rings? In this paper, we characterize strongly clean
von Neumann algebras and prove that all finite von Neumann algebras and all
separable infinite factors are clean.