IMI/Publicaţii/BASM/Ediţii/BASM n.3 (34), 2000/

On subhereditary radicals and Brown-McCoy semisimple rings (English)

Authors: Tumurbat S., Wiegandt R.


The role of essential left ideals is explored in connection with subhereditary radicals and the Brown-McCoy radical. Subhereditary upper radicals $\Cal{UM}$ are characterized by conditions imposed on the class $\Cal M$. We scrutinize the effect of Brown-McCoy semisimplicity of essential left ideals. In this way we characterize simple rings with unity element. If a ring $A \neq 0$ has a Brown-McCoy semisimple essential left ideal then $A$ is Behrens semisimple. Using the notions of representable ideals, special and completely non-special rings ([1, 6, 10]) and that the Brown-McCoy radical is not subhereditary [2], we get a fair amount of information on the structure of Brown-McCoy radical rings possessing a Brown-McCoy semisimple essential left ideal.

S.Tumurbat Department of Algebra University of Mongolia P.O.Box75,
Ulaan Baatar 20, Mongolia
A.Renyi Institute of Mathematics
Hungarian Academy of
P.O. Box 127, H-1364 Budapest Hungary