# 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 Bimodule 2013-03-22 12:01:18 2013-03-22 12:01:18 mps (409) mps (409) 9 mps (409) Definition msc 16D20 sub-bimodule subbimodule