Volume 35 • Number 3 • 2012   • Some Generalizations of Small Injective Modules Truong Cong Quynh Abstract. Let $R$ be a ring. Let $m$ and $n$ be positive integers, a right $R$-module $M$ is called {\it $(m, n)$-small injective}, if every right $R$-homomorphism from an $n$-generated submodule of $J^m$ to $M$ extends to one from $R^m$ to $M$. A ring $R$ is called right $(m, n)$-small injective if the right $R$ module $R_R$ is $(m, n)$-small injective. In this paper, we give some properties of $(m, n)$-small injective modules and right $(m, n)$-small injective rings. 2010 Mathematics Subject Classification: Primary: 16D50, 16D70, 16D80. Full text: PDF