Sifat Rantai Naik pada Modul r-Noetherian serta Keterkaitan Modul r-Noetherian dengan Modul Noetherian dan Modul Hampir Noetherian

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