On cleanness of AW*-algebras
Operator Algebras
2025-04-21 v1
Abstract
A ring is called clean if every element is the sum of an invertible element and an idempotent. This paper investigates the cleanness of AW*-algebras. We prove that all finite AW*-algebras are clean, affirmatively solving a question posed by Vas. We also prove that all countably decomposable infinite AW*-factors are clean. A *-ring is called almost *-clean if every element can be expressed as the sum of a non-zero-divisor and a projection. We show that an AW*-algebra is almost *-clean if and only if it is finite.
Cite
@article{arxiv.2504.13470,
title = {On cleanness of AW*-algebras},
author = {Lu Cui and Minghui Ma},
journal= {arXiv preprint arXiv:2504.13470},
year = {2025}
}