On simple factorization of invertible matrices

Let I be an ideal of a ring R. We say that R is a generalized I-stable ring provided that aR+bR=R with a?∈?1+I,b?∈?R implies that there exists a y?∈?R such that a+by?∈?K(R), where K(R)={x?∈?R?∣?? s, t?∈?R such that sxt=1}. Let R be a generalized I-stable ring. Then every A?∈?GL_n (I) is the product of 13n?12 simple matrices. Furthermore, we prove that A is the product of n simple matrices if I has stable rank one. This generalizes the results of Vaserstein and Wheland on rings having stable rank one.