On Extension Of Simple J-injective Rings And Generalizations Of (m,n)-injective Rings

In this paper, Simple J-injective rings and their extensions are investigated, and (m,n)-injective rings are generalized. There are two sections in this paper. In section one, We characterize when matrix ring, upper triangular matrix ring and trivial extension are simple J-injective rings. We also study almost excellent extension and Spilt null extension of simple J-injective rings. And some characterizations of simple J-injective rings are given. In section two, The concept of (I,K)-(m,n)-injective ring is defined and some characterizations and equivalent conditions are given. Moreover, (I,K)-(m,n)-injective rings are investigated and discussed.