The Schröder-Bernstein problem for relative injective modules

Abstract

Let $(K,\M)$ be a pair satisfying some mild condition, where $K$ is a class of $R$-modules and $\M$ is a class of $R$-homomorphisms. We show that if $f:A\rightarrow B$ and $g:B\rightarrow A$ are $\M$-embeddings and $A,B$ are $K_\M$-injective, then $A$ is isomorphic to $B$, positively answering an question proposed by Marcos and Jiri [6].