Abstract
LetRbe a ring andMa rightR-module. It is shown that (1)δ(M)is Noetherian if and only ifMsatisfies ACC onδ-small submodules; (2)δ(M)is Artinian if and only ifMsatisfies DCC onδ-small submodules; (3)Mis Artinian if and only ifMis an amplyδ-supplemented module and satisfies DCC onδ-supplement submodules and onδ-small submodules.
Subject
Mathematics (miscellaneous)
Cited by
7 articles.
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1. Some Variations of -Supplemented Modules with Regard to a Hereditary Torsion Theory;Journal of Mathematics;2023-10-12
2. ƒ-small submodules ƒ-supplemented modules;2ND INTERNATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND APPLICATIONS: ICMTA2021;2023
3. f-Hollow modules;Journal of Physics: Conference Series;2022-08-01
4. Her $\delta-$ Eşatomik Genişlemede $\delta-$ Tümleyene Sahip Modüller;Sinop Üniversitesi Fen Bilimleri Dergisi;2019-06-27
5. G–
$$\delta$$
δ
–M Modules and Torsion Theory Cogenerated by Such Modules;Iranian Journal of Science and Technology, Transactions A: Science;2017-03-27