# direct summand

Let $R$ be a ring and $B\subseteq A$ left (right) $R$-modules. Then $B$ is called a *direct summand ^{}* of $A$ if there exists a left (right) $R$-submodule

^{}$C$ such that $A=B\oplus C$.

For example, a projective module^{} is a direct summand of a free module^{} over any ring.

Title | direct summand |
---|---|

Canonical name | DirectSummand |

Date of creation | 2013-03-22 14:51:42 |

Last modified on | 2013-03-22 14:51:42 |

Owner | CWoo (3771) |

Last modified by | CWoo (3771) |

Numerical id | 6 |

Author | CWoo (3771) |

Entry type | Definition |

Classification | msc 16D10 |

Related topic | DirectSum |