摘要
F.A.Szasz has put forward the open problem 55 in [1]: Let K be the class of all subdirectly irreducible rings, whose Jacobson radical is (0). Examine the upper radical determined by the class K. In this paper, the problem has been examined. (1) It has been proved that the upper radical R determined by the class K is a special radical,which lies between Jacobson radical and Brown-McCoy radical. (2) It has been given some necessary and sufficient condition of ring A to be an R-radical ring.
Ｆ．Ａ．Ｓｚａｓｚ在［１］中提出公开问题５５：设Ｋ是Ｊａｃｏｂｓｏｎ根为零的全体亚直既约环类，研究类Ｋ确定的上根．本文对此进行了研究，证明了Ｊａｃｏｂｓｏｎ根为零的全体亚直既约环类Ｋ确定的上根Ｒ是特殊根，它介于Ｊａｃｏｂｓｏｎ根与Ｂｒｏｗｎ－ＭｃＣｏｙ根之间．并给出任意结合环Ａ为Ｒ－根环的充要条件．
