Commutative Bezout domains of stable range 1.5

Abstract

A ring R is said to be of stable range 1.5 if for each a, b ∈ R and 0 = c ∈ R satisfying aR+ bR+ cR = R there exists r ∈ R such that (a+ br)R+ cR = R. Let R be a commutative domain in which all finitely generated ideals are principal, and let R be of stable range 1.5. Then each matrix A over R is reduced to Smith's canonical form by transformations P AQ in which P and Q are invertible and at least one of them can be chosen to be a product of elementary matrices. We generalize Helmer's theorem about the greatest common divisor of entries of A over R.