Reduction of Matrices over Bezout Rings of Stable Rank not Higher than 2

  • B. V. Zabavskii

Abstract

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.
Published
25.04.2003
How to Cite
ZabavskiiB. V. “Reduction of Matrices over Bezout Rings of Stable Rank Not Higher Than 2”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 55, no. 4, Apr. 2003, pp. 550-4, https://umj.imath.kiev.ua/index.php/umj/article/view/3929.
Section
Research articles