### Abstract

Let R be a commutative ring with identity and M an R-module. We introduce and give some properties and characterizations of the concepts of Mcancellation, M-weak cancellation, M-meet principal, and M-weak meet principal ideals. We prove that a submodule of a faithful multiplication module is faithful (resp. finitely generated, multiplication, flat, projective, pure, prime) if and only if its residual by a finitely generated faithful multiplication ideal is a faithful (resp. finitely generated, multiplication, flat, projective, pure, prime) submodule.

Original language | English |
---|---|

Pages (from-to) | 405-422 |

Number of pages | 18 |

Journal | Beitrage zur Algebra und Geometrie |

Volume | 46 |

Issue number | 2 |

Publication status | Published - 2005 |

### Keywords

- Cancellation ideal
- Meet-principal ideal
- Multiplication module
- Residual submodule

### ASJC Scopus subject areas

- Algebra and Number Theory
- Geometry and Topology

## Fingerprint Dive into the research topics of 'Residual submodules of multiplication modules'. Together they form a unique fingerprint.

## Cite this

Ali, M. M. (2005). Residual submodules of multiplication modules.

*Beitrage zur Algebra und Geometrie*,*46*(2), 405-422.