Bimodule

Let $𝑅, 𝑇$ be 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

(𝑟 𝑚) 𝑡 = 𝑟 (𝑚 𝑡)

An $(𝑅, 𝑅)$ -bimodule is also called an $𝑅$ -bimodule.

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