Exchange General Rings with Bounded Indices are Clean

Weixing Chen

Abstract

It is proven that an exchange general ring with bounded index is a clean general ring. In particular, an ideal I with bounded index in an exchange
ring R is a clean ideal, which gives a positive answer to a question of H. Chen and M. Chen (Internat. J. Math. Math. Sci. 2003). Moreover, it is proven that each bounded matrix over an exchange ring R is a sum of an invertible matrix and an idempotent matrix, extending one of the main results of S. Wang and H. Chen (Bull. Korean Math. Soc. 43(1)(2006)).