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. 
@article{ADM_2014_18_1_a10,
     author = {Oswaldo Lezama and Claudia Gallego},
     title = {Matrix approach to noncommutative stably free modules and {Hermite} rings},
     journal = {Algebra and discrete mathematics},
     pages = {109--137},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2014_18_1_a10/}
}
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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/