Lu CuiAcademy of Mathematics and Systems Science, Chinese Academy of SciencesLinzhe HuangTsinghua University, YMSCWenming WuSchool of Mathematical Sciences, Chongqing Normal UniversityWei YuanAcademy of Mathematics and Systems Science, Chinese Academy of SciencesHanbin ZhangSchool of Mathematics (Zhuhai), Sun Yat-sen University
Journal of Mathematical Analysis and Applications, 21, 2022.4
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.