A Survey of Strongly Clean Rings

作者：Yang Xiande^*

来源：Acta Applicandae Mathematicae, 2009, 108(1): 157-173.

DOI：10.1007/s10440-008-9364-6

• Strongly clean ring
• Matrix ring
• Strongly pi-regular ring
• Uniquely strongly clean ring
• Power series ring
• Strongly clean general ring

Let R be an associative ring with identity. An element aaR is called clean if a=e+u with e an idempotent and u a unit of R and a is called strongly clean if, in addition, eu=ue. A ring R is called clean if every element of R is clean and R is strongly clean if every element of R is strongly clean. In the paper [Nicholson and Zhou, Clean rings: a survey, Advances in Ring Theory, 181-198, World Sci. Pub., Hackensack, NJ, 2005], the authors brought out an up to date account of the results in the study of clean rings. Here, we give an account of the results on strongly clean rings.

• 出版日期2009-10
• 单位哈尔滨工业大学