Geodesic
Two remarks on critical associative rings
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (1982), pp. 24-28

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Let $A$ be a critical ring, $R$ its Jacobson radical and $A/R\cong B_1\oplus\dots\oplus B_k$ being simple. We prove that $k$ is at most the nilpotency class of $R$. Then we study when the ring of triangular matrices over a critical ring with unity is critical. 
@article{VMUMM_1982_2_a6,
     author = {P. N. Siderov},
     title = {Two remarks on critical associative rings},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {24--28},
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     number = {2},
     year = {1982},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_2_a6/}
}
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P. N. Siderov. Two remarks on critical associative rings. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (1982), pp. 24-28. http://geodesic.mathdoc.fr/item/VMUMM_1982_2_a6/