Let R and S be rings. An (R,S)-bimodule is an abelian groupMathworldPlanetmath M which is a left module over R and a right module over S such that the r(ms)=(rm)s holds for each r in R, m in M, and s in S. Equivalently, M is an (R,S)-bimodule if it is a left module over RSop or a right module over RopS.

When M is an (R,S)-bimodule, we sometimes indicate this by writing the module as MSR.

If P is a subgroupMathworldPlanetmathPlanetmath of M which is also an (R,S)-bimodule, then P is an (R,S)-subbimodule of M.

Title bimodule
Canonical name Bimodule
Date of creation 2013-03-22 12:01:18
Last modified on 2013-03-22 12:01:18
Owner mps (409)
Last modified by mps (409)
Numerical id 9
Author mps (409)
Entry type Definition
Classification msc 16D20
Synonym sub-bimodule
Defines subbimodule