Geodesic
Necessary conditions for solvability of a system of linear equations over a ring
Diskretnaya Matematika, Tome 16 (2004) no. 2, pp. 44-53.

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Necessary conditions for solvability of systems of linear equations over associative rings are considered. In some cases, these conditions are also sufficient for solvability of systems. This research was supported by the grant 2358.2003.9 of the President of Russian Federation for supporting the leading scientific schools. 
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V. P. Elizarov. Necessary conditions for solvability of a system of linear equations over a ring. Diskretnaya Matematika, Tome 16 (2004) no. 2, pp. 44-53. http://geodesic.mathdoc.fr/item/DM_2004_16_2_a2/

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