[[Module theory MOC]]
# Bimodule

Let $R,T$ be [[ring|rings]], possibly non-commutative.
An $(R,T)$-**bimodule** $M$ is both a left $R$-[[module]] and right $T$-module,
such that for any $r \in R$, $t \in T$, and $m \in M$ #m/def/module 
$$
\begin{align*}
(rm)t = r(mt)
\end{align*}
$$
An $(R,R)$-bimodule is also called an $R$-bimodule.

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#state/develop | #lang/en | #SemBr