Reduction of Matrices over Bezout Rings of Stable Rank not Higher than 2 - Zabavskii, B. V. (Ukrains’kyi Matematychnyi Zhurnal, 2003)
We prove that a commutative Bezout ring is an Hermitian ring if and only if it is a Bezout ring of stable rank 2. It is shown that a noncommutative Bezout ring of stable rank 1 is an Hermitian ring. This implies that a noncommutative semilocal Bezout ring is an Hermitian ring. We prove that the Bezout domain of stable rank 1 with two-element group of units is a ring of elementary divisors if and only if it is a duo-domain.