It is known that a simple Bézout domain is a domain of elementary divisors if and only if it is 2-simple. We prove that, over a 2-simple Ore domain of stable rank 1, an arbitrary matrix that is not a divisor of zero is equivalent to a canonical diagonal matrix.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 10, pp. 1436–1440, October, 2010.
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Domsha, O.V., Zabavs’kyi, B.V. 2-Simple ore domains of stable rank 1. Ukr Math J 62, 1666–1672 (2011). https://doi.org/10.1007/s11253-011-0458-3
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DOI: https://doi.org/10.1007/s11253-011-0458-3