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 pro...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.展开更多
We introduce the graded version of the antisimple primitive radical SJ, the graded an- tisimple prinfitive radical SJ_G. We show that SJ_G=SJ_(ref)=SJ^G when |G|<∞. where SJ_(ref) denotes the reflected antisimple ...We introduce the graded version of the antisimple primitive radical SJ, the graded an- tisimple prinfitive radical SJ_G. We show that SJ_G=SJ_(ref)=SJ^G when |G|<∞. where SJ_(ref) denotes the reflected antisimple primitive radical and SJ^G denotes the restricted antisimple primitive radical. Furthermore, we discuss the graded supplementing radical of SJ^G.展开更多
文摘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.
基金Project supported by the National Natural Science Foundation of China (No: 19971073)the Natural Science Foundation of Jiangsu Province.
文摘We introduce the graded version of the antisimple primitive radical SJ, the graded an- tisimple prinfitive radical SJ_G. We show that SJ_G=SJ_(ref)=SJ^G when |G|<∞. where SJ_(ref) denotes the reflected antisimple primitive radical and SJ^G denotes the restricted antisimple primitive radical. Furthermore, we discuss the graded supplementing radical of SJ^G.
