On Strongly Clean General Rings
Received:November 18, 2005  Revised:July 03, 2006
Key Words: strongly clean general ring, strongly $\pi$-regular general ring, upper triangular matrix ring.
Fund Project:the Foundation for Excellent Doctoral Dissertation of Southeast University (YBJJ0507); the National Natural Science Foundation of China (10571026); the Natural Science Foundation of Jiangsu Province (Bk2005207).
 Author Name Affiliation WANG Zhou Department of Mathematics, Southeast University, Jiangsu 210096, China CHEN Jian-long Department of Mathematics, Southeast University, Jiangsu 210096, China
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In this paper, we introduce the concept of strongly clean general ring (with or without unity) and extend some of the basic results to a wider class. We prove that every strongly $\pi$-regular general ring is strongly clean and the corner of the strongly clean general ring is strongly clean. It is also proved that upper triangular matrix rings of the commutative clean general ring with $J(I)=Q(I)$ are strongly clean.