It is shown that an adequate ring with nonzero Jacobson radical has a stable range 1. A class of matrices over an adequate ring with stable range 1 is indicated.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 11, pp. 1575–1578, November, 2009.
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Zabavs’kyi, B.V., Petrychkovych, V.M. On the stable range of matrix rings. Ukr Math J 61, 1853–1857 (2009). https://doi.org/10.1007/s11253-010-0317-7
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DOI: https://doi.org/10.1007/s11253-010-0317-7