bimodule
Sign in to saveIn abstract algebra, a bimodule is an abelian group that is both a left and a right module, such that the left and right multiplications are compatible. Besides appearing naturally in many parts of mathematics, bimodules play a clarifying role, in the sense that many of the relationships between left and right modules become simpler when they are expressed in terms of bimodules.
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- Definition
- Examples
- Further notions and facts
- See also
- References
In abstract algebra, a bimodule is an abelian group that is both a left and a right module, such that the left and right multiplications are compatible. Besides appearing naturally in many parts of mathematics, bimodules play a clarifying role, in the sense that many of the relationships between left and right modules become simpler when they are expressed in terms of bimodules.
== Definition == If R and S are two rings, then an R-S-bimodule is an abelian group such that: M is a left R-module with an operation · and a right S-module with an operation *. For all r in R, s in S and m in M: (r\cdot m)*s = r\cdot (m*s) .