Abstract:
If L(R) is a set of left ideals defined in any ring R, we say that
R is L-stable if it has stable range 1 relative to the set L(R). We explore
L-stability in general, characterize when it passes to related classes of rings,
and explore which classes of rings are L-stable for some L. Some well known
examples of L-stable rings are presented, and we show that the Dedekind finite
rings are L-stable for a suitable L.
