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-range conditions, under which a commutative Bézout domain is a domain of elementary divisors.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 1, pp. 126–139, January, 2012.
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Shchedryk, V.P. Commutative domains of elementary divisors and some properties of their elements. Ukr Math J 64, 140–155 (2012). https://doi.org/10.1007/s11253-012-0634-0
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DOI: https://doi.org/10.1007/s11253-012-0634-0