The Baer Radical Of Generalized Matrix Rings

In this paper, we introduce a new concept of generalized matrix rings and build up the general theory of radicals for g.m.rings. Meantime, we obtain $${\bar{r}}_b(A)=g\mathrm{.}m\mathrm{.}{r}_b(A)=\sum \{r_b(A_{ij})\mid i,j\in I\}=r_b(A)$$