Module theory MOC

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 ∈𝑅, 𝑡 ∈𝑇, and 𝑚 ∈𝑀 module

(𝑟𝑚)𝑡=𝑟(𝑚𝑡)

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

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