摘要
本文介绍了强clean—般环的概念并将一些基本的结果推广到这个更广的环类．证明了强clean一般环的角落环和强π-正则一般环都是强clean的,还讨论了强clean一般环的扩张并且证明了满足条件J(I)=Q(I)的交换clean一般环的上三角矩阵环是强clean的．
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 π-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.
基金
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).
关键词
强clean一般环
强π-正则一般环
上三角矩阵环
strongly clean general ring, strongly π-regular general ring, upper triangular matrix ring.
