We introduce the notion of a ring of almost unit stable rank 1 as a generalization of the notion of a ring of unit stable rank 1. We prove that a ring of almost unit stable rank 1 with nonzero Jacobson radical is a ring of unit stable rank 1 and is a 2-good ring. We introduce the notion of almost 2-good ring and show that an adequate domain is an almost 2-good ring.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 6, pp. 840–843, June, 2011.
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Vasyunyk, I.S., Zabavs’kyi, B.V. Rings of almost unit stable rank 1. Ukr Math J 63, 977–980 (2011). https://doi.org/10.1007/s11253-011-0557-1
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DOI: https://doi.org/10.1007/s11253-011-0557-1