| 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.
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| 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). |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2007.01.005 |
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