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 $R\otimes\opposite{S}$ or a right module over $\opposite{R}\otimes S$ .

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

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