Commutative domains of elementary divisors and some properties of their elements
We study commutative domains of elementary divisors from the viewpoint of investigation of the structure of invertible matrices that reduce a given matrix to the diagonal form. Some properties of elements of these domains are indicated. We establish conditions, close to the stable-rank conditions, under which a commutative Bezout domain is a domain of ´ elementary divisors.
English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 1, pp 140-155.
Citation Example: Shchedrik V. P. Commutative domains of elementary divisors and some properties of their elements // Ukr. Mat. Zh. - 2012. - 64, № 1. - pp. 126-139.