Clean Semiprime f-Rings with Bounded Inversion
نویسنده
چکیده
An element in a ring is called clean if it may be written as a sum of a unit and idempotent. The ring itself is called clean if every element is clean. Recently, Anderson and Camillo (Anderson, D. D., Camillo, V. (2002). Commutative rings whose elements are a sum of a unit and an idempotent. Comm. Algebra 30(7):3327–3336) has shown that for commutative rings every von-Neumann regular ring as well as zero-dimensional rings are clean. Moreover, every clean ring is a pm-ring, that is every prime ideal is contained in a unique maximal ideal. In the same article, the authors give an example of a commutative ring which is a pm-ring yet not clean, e.g., C(R). It is this example which interests us. Our discussion shall take place in a more general setting. We assume that all rings are commutative with 1. *Correspondence: Warren Wm. McGovern, Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA; E-mail: [email protected]. COMMUNICATIONS IN ALGEBRA Vol. 31, No. 7, pp. 3295–3304, 2003
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