Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (1982), pp. 24-28
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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/
@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},
year = {1982},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_2_a6/}
}
TY - JOUR
AU - P. N. Siderov
TI - Two remarks on critical associative rings
JO - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY - 1982
SP - 24
EP - 28
IS - 2
UR - http://geodesic.mathdoc.fr/item/VMUMM_1982_2_a6/
LA - ru
ID - VMUMM_1982_2_a6
ER -
%0 Journal Article
%A P. N. Siderov
%T Two remarks on critical associative rings
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 1982
%P 24-28
%N 2
%U http://geodesic.mathdoc.fr/item/VMUMM_1982_2_a6/
%G ru
%F VMUMM_1982_2_a6
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.
