# 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 |