A NOTE ON STRONGLY CLEAN MATRIX RINGS

作者：Fan Lingling; Yang Xiande^*

来源：Communications in Algebra, 2010, 38(3): 799-806.

DOI：10.1080/00927870802570693

• Group ring
• Local ring
• Matrix ring
• Strongly clean ring

Let R be an associative ring with identity. An element a. R is called strongly clean if a = e + u with e(2) = e is an element of R, u a unit of R, and eu = ue. A ring R is called strongly clean if every element of R is strongly clean. Strongly clean rings were introduced by Nicholson [7]. It is unknown yet when a matrix ring over a strongly clean ring is strongly clean. Several articles discussed this topic when R is local or strongly pi-regular. In this note, necessary conditions for the matrix ring IM(n)(R) (n > 1) over an arbitrary ring R to be strongly clean are given, and the strongly clean property of IM(2) (RC(2)) over the group ring RC(2) with R local is obtained.

• 出版日期2010
• 单位哈尔滨工业大学