Extensions of rings with many units

摘要

In this paper, we investigate stable range conditions over extensions of matrix rings. It is shown that a ring R satisfies (s, 2)-stable range if and only if R has a complete orthogonal set {e(1),..., e(n)} of idempotents such that all e(i)Re(i) satisfy (s, 2)-stable range. Also we extend this result to (s, 2)-rings and rings satisfying unit 1-stable range. References: 14