Geodesic
Isomorphisms of general linear groups over associative rings graded by an Abelian group
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 3, pp. 5-40 
A. S. Atkarskaya; E. I. Bunina; A. V. Mikhalev. Isomorphisms of general linear groups over associative rings graded by an Abelian group. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 3, pp. 5-40. http://geodesic.mathdoc.fr/item/FPM_2010_16_3_a0/
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     title = {Isomorphisms of general linear groups over associative rings graded by an {Abelian} group},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we give a simpler proof of the Golubchik–Mikhalev–Zelmanov theorem on the structure of isomorphisms between general linear groups over associative rings, and also prove an extension of this theorem for linear groups over rings graded by an Abelian group.

[1] Balaba I. N., “Izomorfizmy graduirovannykh kolets endomorfizmov proobrazuyuschikh”, Fundament. i prikl. mat., 13:1 (2007), 3–10 | MR | Zbl

[2] Golubchik I. Z., Lineinye gruppy nad assotsiativnymi koltsami, Dis. $\dots$ dokt. fiz.-mat. nauk, Ufa, 1997

[3] Golubchik I. Z., Mikhalëv A. V., “Izomorfizmy polnoi lineinoi gruppy nad assotsiativnym koltsom”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 1983, no. 3, 61–72 | MR | Zbl

[4] Zelmanov E. I., “Izomorfizmy lineinykh grupp nad assotsiativnym koltsom”, Sib. mat. zhurn., 26:4 (1985), 49–67 | MR | Zbl

[5] Feis K., Koltsa, moduli, kategorii, Mir, M., 1979 | MR

[6] Nastasescu C., van Oystaeyen F., Graded Ring Theory, North-Holland, Amsterdam, 1982 | MR | Zbl