Definition 10.11.6. An abelian group $N$ is called an $(A, B)$-bimodule if it is both an $A$-module and a $B$-module, and the actions $A \to End(M)$ and $B \to End(M)$ are compatible in the sense that $(ax)b = a(xb)$ for all $a\in A, b\in B, x\in N$. Usually we denote it as $_ AN_ B$.
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