Sifat rantai naik pada modul r-noetherian serta keterkaitan modul r-noetherian dengan modul noetherian dan modul hampir noetherian

Az-Zakiyah, Qurratul Aini and Nisfulaila, Intan (2024) Sifat rantai naik pada modul r-noetherian serta keterkaitan modul r-noetherian dengan modul noetherian dan modul hampir noetherian. Jurnal Riset Mahasiswa Matematika, 3 (6). pp. 289-295. ISSN 2808-4926

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Abstract

Modules are algebraic structures formed from Abelian groups and rings as scalars. A module is a Noetherian module if it satisfies the ascending chain condition on its submodules. An R-module M is called an almost Noetherian module if every true submodule in M is finitely generated. There is a new class of r-Noetherian modules. Let\ R be a ring and M an R-module, M is said to be an r-Noetherian module if every r-submodule of M is finitely generated. The symbol r refers to the true ideal of the ring with Ann\ a=0. The properties to be studied are the ascending chain properties of r-Noethetian modules. Furthermore,, the relationship of r-Noetherian module with Noetherian module and almost Noetherian module will be studied. This research uses a literature study approach. The stages carried out in this study begin with completing the proof of the lemma relating to the ascending chain on the r-Noetherian Module. Furthermore, completing the proof of the proposition regarding the relationship of the r-Noetherian module with the Noetherian module and almost Noetherian module. The property of ascending chain on r-Noetherian module is that every ascending chain line of r-submodules on r-Noetherian module will stop at a finite step. Furthermore, the connection of r-Noetherian module with Noetherian module and almost Noetherian module is mutual subset

Item Type:	Journal Article
Keywords:	ascending chain; linkage; r-Noetherian module; Noetherian module; almost Noetherian module.
Subjects:	01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010199 Pure Mathematics not elsewhere classified
Divisions:	Faculty of Mathematics and Sciences > Department of Mathematics
Depositing User:	Intan Nisfulaila
Date Deposited:	09 Dec 2025 13:22

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