Bezout rings of stable ranк 1.5 and the decomposition of a complete linear group into its multiple subgroups - Shchedrik, V. P. (Ukrains’kyi Matematychnyi Zhurnal, 2017)
A ring R is called a ring of stable rank 1.5 if, for any triple a, b, c R, c ot = 0, such that aR + bR + cR = R, there exists r R such that (a + br)R + cR = R. It is proved that a commutative Bezout domain has a stable rank 1.5 if and only if every invertible matrix A can be represented in the form A = HLU, where L, U are elements of the groups of lower and upper unitriangular matrices (triangular matrices with 1 on the diagonal) and the matrix H belongs to the group G Φ = { H GLn(R) | H_1 GL_n(R) : HΦ = Φ H_1}, where Φ = diag (φ 1, φ 2,..., φ n), φ 1| φ 2| ... | φ n, φ n ot = 0.