### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory
- Geometry and Topology

### Cite this

*Beitrage zur Algebra und Geometrie*,

*46*(2), 405-422.

**Residual submodules of multiplication modules.** / Ali, Majid M.

Research output: Contribution to journal › Article

*Beitrage zur Algebra und Geometrie*, vol. 46, no. 2, pp. 405-422.

}

TY - JOUR

T1 - Residual submodules of multiplication modules

AU - Ali, Majid M.

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

KW - Cancellation ideal

KW - Meet-principal ideal

KW - Multiplication module

KW - Residual submodule

UR - http://www.scopus.com/inward/record.url?scp=30644467347&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=30644467347&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:30644467347

VL - 46

SP - 405

EP - 422

JO - Beitrage zur Algebra und Geometrie

JF - Beitrage zur Algebra und Geometrie

SN - 0138-4821

IS - 2

ER -