Abstract
An ideal I of a ring R is generalized stable in case aR + bR = R with a ∈ I, b ∈ R implies that there exist s, t ∈ 1 + I such that s(a + by)t = 1 for a y ∈ R. We establish, in this article, necessary and sufficient conditions for an ideal of a regular ring to be generalized stable. It is shown that every regular square matrix over such ideals admits a diagonal reduction. These extend the corresponding results of generalized stable regular rings.
ACKNOWLEDGMENTS
The author would like to thank the referee for his/her many corrections and suggestions, which considerably improved article and lead to the new version.
Notes
Communicated by J. L. Gomez Pardo.