Stable range one for rings with many units
Here is the first stable range condition for a ring R with 1 (introduced by H. Bass): If a, b are in R and \(aR+bR=R\), then there is y in R such that \(R(a+by)=R\). In a stronger condition called in the paper (right) unit 1-stable range condition, one requires the above y to be a unit of R. Here is an even stronger condition: for any a, b in R there is a unit u of R such that a-u and \(b-u^{-1}\) are both units. This condition is verified in the paper in a number of interesting cases. For any unital complex C *-algebra R, the above 3 conditions are equivalent.
strongly \(\pi \) -regular von Neumann regular rings
scientific article; zbMATH DE number 4065201
scientific article