Geodesic
Multiplicative groups of finitely generated irreducible matrix rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 3, pp. 843-849 
A. M. Popova. Multiplicative groups of finitely generated irreducible matrix rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 3, pp. 843-849. http://geodesic.mathdoc.fr/item/FPM_1999_5_3_a13/
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     author = {A. M. Popova},
     title = {Multiplicative groups of finitely generated irreducible matrix rings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {843--849},
     year = {1999},
     volume = {5},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1999_5_3_a13/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In famous L. Fuchs' monograph about infinite abelian groups the problem of description of groups of invertible elements of associative rings with unit was formulated. This article contains a part of solution of the problem for any finitely generated matrix rings over the field of rational numbers. The case of irreducible rings over $Q$ is considered in this article. The effective description of multiplicative groups of such rings in terms of generating elements is given.