This paper answers, in the negative, Open Problem 4 in Goodearl's book on von Neumann regular rings: a directly finite regular ring R with s-comparability is constructed which is not unit-regular. It is shown, however, that the behaviour of these rings R is still quite good. They have cancellation of small projective modules and, in particular, their stable range is at most 2.
|Journal||Journal of Pure and Applied Algebra|
|Publication status||Published - 26 Feb 1996|
- Hermite ring
- Stable range
- Unit-regular ring
- Von Neumann regular ring