IMCS/Publications/BASM/Issues/BASM n.1 (44), 2004/

Radicals around Kothe's problem.

Authors: S. Tumurbat, R. Wiegandt


Radicals gamma will be studied for which the condition A[x] belongs to gamma for all nil rings A is equivalent to the positive solution of Kothe's Problem (A[x] is Jacobson radical for all nil rings A, in Krempa's formulation). The closer gamma is to the Jacobson radical, the better approximation of the positive solution is obtained. Seeking, however, for a negative solution, possibly large radicals gamma are of interest. In this note such large radicals will be studied.

S. Tumurbat
Department of Algebra, University of Mongolia
P.O. Box 75, Ulaan Baatar 20, Mongolia
R. Wiegandt A. Renyi
Institute of Mathematics Hungarian Academy of Sciences
P.O. Box 127,
H-1364 Budapest, Hungary


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