标题： 关于AW*-代数的清洁性 显示英文标题

标题： On cleanness of AW*-algebras

摘要： 环被称为干净的，如果每个元素都可以表示为一个可逆元和一个幂等元之和。 本文研究了AW*-代数的干净性。 我们证明所有有限的AW*-代数都是干净的，解决了Vas提出的问题。 我们还证明所有可数分解的无限AW*-因子也是干净的。 *环被称为几乎*干净的，如果每个元素都可以表示为一个非零除元和一个投影之和。 我们证明AW*-代数是几乎*干净的当且仅当它是有限的。 显示英文摘要

摘要： 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.