### Abstract

All rings are commutative with identity and all modules are unital. The tensor product of projective (resp. flat, multiplication) modules is a projective (resp. flat, multiplication) module but not conversely. In this paper we give some conditions under which the converse is true. We also give necessary and sufficient conditions for the tensor product of faithful multiplication Dedekind (resp. Prüfer, finitely cogenerated, uniform) modules to be a faithful multiplication Dedekind (resp. Prüfer, finitely cogenerated, uniform) module. Necessary and sufficient conditions for the tensor product of pure (resp. invertible, large, small, join principal) submodules of multiplication modules to be a pure (resp. invertible, large, small, join principal) submodule are also considered.

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

Pages (from-to) | 305-327 |

Number of pages | 23 |

Journal | Beitrage zur Algebra und Geometrie |

Volume | 47 |

Issue number | 2 |

Publication status | Published - 2006 |

### Fingerprint

### Keywords

- Cancellation module
- Flat module
- Invertible submodule
- Join principal submodule
- Large submodule
- Multiplication module
- Projective module
- Pure submodule
- Small submodule
- Tensor product

### ASJC Scopus subject areas

- Algebra and Number Theory
- Geometry and Topology

### Cite this

*Beitrage zur Algebra und Geometrie*,

*47*(2), 305-327.

**Multiplication modules and tensor product.** / Ali, Majid M.

Research output: Contribution to journal › Article

*Beitrage zur Algebra und Geometrie*, vol. 47, no. 2, pp. 305-327.

}

TY - JOUR

T1 - Multiplication modules and tensor product

AU - Ali, Majid M.

PY - 2006

Y1 - 2006

N2 - All rings are commutative with identity and all modules are unital. The tensor product of projective (resp. flat, multiplication) modules is a projective (resp. flat, multiplication) module but not conversely. In this paper we give some conditions under which the converse is true. We also give necessary and sufficient conditions for the tensor product of faithful multiplication Dedekind (resp. Prüfer, finitely cogenerated, uniform) modules to be a faithful multiplication Dedekind (resp. Prüfer, finitely cogenerated, uniform) module. Necessary and sufficient conditions for the tensor product of pure (resp. invertible, large, small, join principal) submodules of multiplication modules to be a pure (resp. invertible, large, small, join principal) submodule are also considered.

AB - All rings are commutative with identity and all modules are unital. The tensor product of projective (resp. flat, multiplication) modules is a projective (resp. flat, multiplication) module but not conversely. In this paper we give some conditions under which the converse is true. We also give necessary and sufficient conditions for the tensor product of faithful multiplication Dedekind (resp. Prüfer, finitely cogenerated, uniform) modules to be a faithful multiplication Dedekind (resp. Prüfer, finitely cogenerated, uniform) module. Necessary and sufficient conditions for the tensor product of pure (resp. invertible, large, small, join principal) submodules of multiplication modules to be a pure (resp. invertible, large, small, join principal) submodule are also considered.

KW - Cancellation module

KW - Flat module

KW - Invertible submodule

KW - Join principal submodule

KW - Large submodule

KW - Multiplication module

KW - Projective module

KW - Pure submodule

KW - Small submodule

KW - Tensor product

UR - http://www.scopus.com/inward/record.url?scp=41549142406&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41549142406&partnerID=8YFLogxK

M3 - Article

VL - 47

SP - 305

EP - 327

JO - Beitrage zur Algebra und Geometrie

JF - Beitrage zur Algebra und Geometrie

SN - 0138-4821

IS - 2

ER -