Title of article :
L-STABLE RINGS
Author/Authors :
Horoub, Ayman M. A Department of Mathematics - University of Calgary Calgary, Canada , Nicholson, W. K Department of Mathematics - University of Calgary Calgary, Canada
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.
Keywords :
Stable range , uniquely generated ring , internal cancellation ring , von Neumann regular ring , unit-regular ring , triangular matrix ring , left idealtors , L L-stable ring
Journal title :
International Electronic Journal of Algebra
