## Definiton ## Let $R$ and $S$ be [[ring]]s. A $R$-$S$-bimodule homomorphism between two $R$-$S$-[[bimodule]]s $A$ and $B$ is a function $f:A \to B$ such that for all $a:A$, $b:A$, $q:R$, $r:R$, $s:S$, and $t:T$, $$f(q a s + r b t) = q f(a) s + r f(b) t$$ ## See also ## * [[bimodule]] * [[ideal (ring theory)]]