Geodesic
Matrix approach to noncommutative stably free modules and Hermite rings
Algebra and discrete mathematics, Tome 18 (2014) no. 1, pp. 109-137.

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In this paper we present a matrix-constructive proof of an Stafford's Theorem about stably free modules over noncommutative rings. Matrix characterizations of noncommutative Hermite and projective-free rings are exhibit. Quotients, products and localizations of Hermite and some other classes of rings close related to Hermite rings are also considered.
Keywords: noncommutative rings and modules, stably free modules, Hermite rings, matrix methods in homological algebra. 
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Oswaldo Lezama; Claudia Gallego. Matrix approach to noncommutative stably free modules and Hermite rings. Algebra and discrete mathematics, Tome 18 (2014) no. 1, pp. 109-137. http://geodesic.mathdoc.fr/item/ADM_2014_18_1_a10/

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