یوسفیان دارانی, احمد
(2018)
*The study of Properties of Reduced Modules.*
University of Mohaghegh Ardabili, University of Mohaghegh Ardabili.

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## Abstract

We introduce reduced modules over a commutative ring and z0-submodules. Let R be a commutative ring and M an R-module. An R-module M is called reduced if M has no nonzero nilpotent elements. A proper submodule N of M is called a z0-submodule if for each m 2 N, the intersection of all minimal prime submodules of M containing m is contained in N. We denote by h(S), for S � M, the set of all minimal prime submodules of M containing S. IfM is a faithful multiplication reduced R-module, then a prime submodule N of M is minimal if and only if for any m 2 N there exists r 2 R n (N :R M) such that rm = 0. Also, for S � M, annR(S)M = ∩ Q, where Q 2 Min(M) n h(S). Moreover, if N is a nilpotent z0-submodule of M, then every prime submodule of M, minimal over N is a prime z0-submodule and N is equal to an intersection of prime z0-submodules. We introduce property A onM and show that, if the R-moduleM satisfies property A, then any submodule N of M is contained in a z0-submodule.

Item Type: | Other |
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Persian Title: | The study of Properties of Reduced Modules |

Persian Abstract: | - |

Subjects: | Research Projects |

Divisions: | Subjects > Faculty of Basic Sciences > Department of Mathematics Faculty of Basic Sciences > Department of Mathematics |

Date Deposited: | 14 Jul 2019 04:48 |

Last Modified: | 14 Jul 2019 04:48 |

URI: | http://repository.uma.ac.ir/id/eprint/8393 |

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