Geodesic
Isomorphisms of the general linear group over an associative ring
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (1983), pp. 61-72

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It is proved that every isomorphism of linear groups $\varphi\colon\mathrm{GL}_n(R)\to\mathrm{GL}_m(S)$ over arbitrary associative rings $R$ and $S$ with $1/2\in R$ and $1/2\in S$ for $n,m\ge3$ is a standard one on a subgroup $\mathrm{GE}_n(R)$ generated by elementary and diagonal matrices. 
@article{VMUMM_1983_3_a11,
     author = {I. Z. Golubchik and A. V. Mikhalev},
     title = {Isomorphisms of the general linear group over an associative ring},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {61--72},
     publisher = {mathdoc},
     number = {3},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1983_3_a11/}
}
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I. Z. Golubchik; A. V. Mikhalev. Isomorphisms of the general linear group over an associative ring. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (1983), pp. 61-72. http://geodesic.mathdoc.fr/item/VMUMM_1983_3_a11/