bimodule

Let R and S be rings. An (R,S)-bimodule is an abelian group 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 $R\otimes S^{\mathrm{op}}$ or a right module over $R^{\mathrm{op}}\otimes S$.

When M is an (R,S)-bimodule, we sometimes indicate this by writing the module as ${}_{R}M_S$.

If P is a subgroup 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