The Stacks project

Definition 10.12.6. 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 $_ AN_ B$.

Comments (1)

Comment #8367 by Laurent Moret-Bailly on

Unless I missed a convention somewhere, all modules are denoted as left modules, so strictly speaking the notation is not defined. I understand all rings are commutative, and the right module notation is convenient here, but maybe a remark would be in order.

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  • 7 comment(s) on Section 10.12: Tensor products

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