On cleanness of von Neumann algebras

Lu Cui Academy of Mathematics and Systems Science, Chinese Academy of Sciences Linzhe Huang Tsinghua University, YMSC Wenming Wu School of Mathematical Sciences, Chongqing Normal University Wei Yuan Academy of Mathematics and Systems Science, Chinese Academy of Sciences Hanbin Zhang School of Mathematics (Zhuhai), Sun Yat-sen University

Functional Analysis mathscidoc:2205.12001

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.
Von Neumann algebras, Clean rings, Idempotents, Projections
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@inproceedings{lu2022on,
  title={On cleanness of von Neumann algebras},
  author={Lu Cui, Linzhe Huang, Wenming Wu, Wei Yuan, and Hanbin Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517121519389605185},
  booktitle={Journal of Mathematical Analysis and Applications},
  pages={21},
  year={2022},
}
Lu Cui, Linzhe Huang, Wenming Wu, Wei Yuan, and Hanbin Zhang. On cleanness of von Neumann algebras. 2022. In Journal of Mathematical Analysis and Applications. pp.21. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517121519389605185.
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