广义矩阵环的特殊根

The special radicals of generalized matrix rings

本文研究广义矩阵环的某些特殊根，即：广义矩阵环的Ｌｅｖｉｔｚｋｉ诣零根ｒｌ，诣零根ｒｋ，Ｊａｃｏｂｓｏｎ根ｒｊ，Ｂｒｏｗｎ－ＭｃＣｏｙ根ｒｂｍ和强素很ｒｓｐｒ，以及研究广义矩阵环Ａ，Ａｊｉ－环Ａｉｊ和环Ａ的特殊根之间的关系，对于环的超幂零根ｒ，我们得到：ｒ（Ａ）＝ｇ．ｍ．ｒ（Ａ）＝ｒ（Ａ），对于Ｌｅｖｉｔｚｋｉ诣零根ｒｌ和Ｊａｃｏｂｓｏｎ根ｒｊ。

We study some radicals of generalized matrix ringS;Levitzki nil radical r1nil radical rk,Jacobson radical njBrown-McCoy radical rbm and strongly prime radical rspr. We establish therelations amons the special radicals of generalized matrix ring A,Aji-ring Aij and ring A. Thefollowing have been obtained:(1 ) r(A) = g. m. r(A) = r(A) for supernilpotent radicals r.for Levitzki nil radical rl and Jacobson radical rj.