关于强Clean一般环 (英)

On Strongly Clean General Rings

中文关键词:  强clean一般环, 强$\pi$-正则一般环, 上三角矩阵环.

英文关键词:strongly clean general ring, strongly $\pi$-regular general ring, upper triangular matrix ring.

中文摘要:

      本文介绍了强clean一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$\pi$-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.

英文摘要:

      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.