nLab central bimodule

If $R$ is a commutative ring then a central bimodule is an $R$-$R$-bimodule whose right action is obtained from the left by precomposing it with the flip of tensor factors.

If $R$ is an associative ring (or more generally an associative $k$-algebra over a ground commutative ring $k$) then a central bimodule is a bimodule whose restriction to a structure of a bimodule over the center $Z(R)$ is central, i.e. the left and right $Z(R)$-bimodule structures coincide. Cf. pdf

category: algebra