Geodesic
On diagonalizability of regular matrices over rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 1, pp. 103-111 
T. V. Golovacheva. On diagonalizability of regular matrices over rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 1, pp. 103-111. http://geodesic.mathdoc.fr/item/FPM_1996_2_1_a2/
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     title = {On diagonalizability of regular matrices over rings},
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     volume = {2},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1996_2_1_a2/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Some results on the problem of the diagonalizability of an arbitrary von Neumann regular matrix over an associative ring with unit are proved. There are constructed two examples of rings which refute the next conjecture of J. Van-Geel and D. Huylebrouck: if $R$ is an ID-ring (i.e. all idempotent matrices over $R$ are diagonalizable) then every von Neumann regular matrix over $R$ is diagonalizable.