On cleanness of AW*-algebras

Lu Cui; Minghui Ma

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arXiv · 2504.13470

On cleanness of AW*-algebras

Lu Cui·Minghui Ma

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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.

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Lu Cui, Minghui Ma. 2025-04-18. On cleanness of AW*-algebras. https://arxiv.org/abs/2504.13470

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