In this paper, we introduce a new concept of generalized matrix rings andbuild up the general theory of radicals for g.m.rings. Meantime, we obtain$$\bar{r}_b(A)=g.m.r_b(A)=\sum\{r_b(A_{ij})\mid i, j\in I\}=r_b(A)$$
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机译：在本文中，我们引入了广义矩阵环的新概念，并建立了g.m.环的根的一般理论。同时，我们获得$$ \ bar {r} _b（A）= g.m.r_b（A）= \ sum \ {r_b（A_ {ij}）\ mid i，j \ in I \} = r_b（A）$$
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