2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102023In 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 $$\bar{r}_b(A)=g.m.r_b(A)=\sum\{r_b(A_{ij})\mid i, j\in I\}=r_b(A)$$8 pagesRings and Algebras16A21, 16A64, 16A66, 16A78text