Reduction of Matrices over Bezout Rings of Stable Rank not Higher than 2
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.
English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 4, pp 665-670.
Citation Example: Zabavskii B. V. Reduction of Matrices over Bezout Rings of Stable Rank not Higher than 2 // Ukr. Mat. Zh. - 2003. - 55, № 4. - pp. 550-554.