Volume 10, Issue 2 (7-2024)
mmr 2024, 10(2): 66-81 |
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Fazaeli Moghimi H, Hakimi Ghalesafa M. Modules whose Lattice of Radical Submodules is Noetherian. mmr 2024; 10 (2) :66-81
URL: http://mmr.khu.ac.ir/article-1-3262-en.html
URL: http://mmr.khu.ac.ir/article-1-3262-en.html
1- University of Birjand , hfazaeli@birjand.ac.ir
2- University of Birjand
2- University of Birjand
Abstract: (49 Views)
In this paper, we investigate radical Noetherian modules as a collection of modules whose lattice of radical submodules is Noetherian. The collection of radical Noetherian modules contains both families of Noetherian and Artinian modules properly. We will show that the set of minimal prime submodules of a radical Noetherian modules is finite. Also a ring $R$ is called radical Noetherian, if $R$ is a radical Noetherian $R$-module. We will prove that a multiplication $R$-module $M$ is radical Noetherian if and only if $R/Ann(M)$ is a radical Noetherian. Moreover, we will give and prove analogs of Cohen and Hilbert basis theorems for radical Noetherian rings.
Keywords: Radical submodule, Radical Noetherian module, Radical Noetherian ring, Multiplication module.
Type of Study: S |
Subject:
alg
Received: 2022/02/17 | Revised: 2024/07/8 | Accepted: 2024/05/15 | Published: 2024/07/7 | ePublished: 2024/07/7
Received: 2022/02/17 | Revised: 2024/07/8 | Accepted: 2024/05/15 | Published: 2024/07/7 | ePublished: 2024/07/7
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