Geodesic
Grothendieck and Whitehead groups of formal matrix rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 1, pp. 173-203.

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For formal matrix rings, we construct some method of calculation of groups $K_0$ and $K_1$ with the use of groups $K_0$ and $K_1$ of original rings. 
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P. A. Krylov; A. A. Tuganbaev. Grothendieck and Whitehead groups of formal matrix rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 1, pp. 173-203. http://geodesic.mathdoc.fr/item/FPM_2015_20_1_a9/

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