A ring R has a stable range 1.5 if, for every triple of left relatively prime nonzero elements a, b, and c in R, there exists r such that the elements a+br and c are left relatively prime. Let R be a commutative Bezout domain. We prove that the matrix ring M 2 (R) has the stable range 1.5 if and only if the ring R has the same stable range.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 6, pp. 849–860, June, 2015.
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Shchedryk, V.P. Bezout Rings of Stable Range 1.5. Ukr Math J 67, 960–974 (2015). https://doi.org/10.1007/s11253-015-1126-9
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DOI: https://doi.org/10.1007/s11253-015-1126-9