Weakly clean rings

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• 作者：Janez 艩ter
• 关键词：16U99 ; 16S70 ; 46L05
• 刊名：Journal of Algebra
• 出版年：1 March, 2014
• 年：2014
• 卷：401
• 期：Complete
• 页码：1-12
• 全文大小：256 K

文摘

We study the class of weakly clean rings which were introduced in . It is known that weakly clean rings are a subclass of exchange rings and that they contain clean rings as a proper subclass. In this paper we prove that weakly clean rings also contain some other important examples of exchange rings, such as 蟺-regular rings and -algebras of real rank zero. Further, we prove that many classes of weakly clean rings can be viewed as corners of clean rings. This, for example, implies that every 蟺-regular ring and every -algebra of real rank zero is a corner of a clean ring. Lastly, we study the question when the ideal extension of weakly clean rings is weakly clean, and we give an example of a non-weakly clean exchange ring, answering the question in .