Δ-Small Submodules and δ-Supplemented Modules. (9th August 2007)

• Record Type: Journal Article
• Authors: Wang Wang, Yongduo Yongduo
• Other Names: Rhemtulla Rhemtulla Akbar Akbar Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Voume 2007(2007)
• Publication Date: 2007-08-09
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2007/58132
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : Let R be a ring and M a right R -module. It is shown that (1) δ ( M ) is Noetherian if and only if M satisfies ACC on δ -small submodules; (2) δ ( M ) is Artinian if and only if M satisfies DCC on δ -small submodules; (3) M is Artinian if and only if M is an amply δ -supplemented module and satisfies DCC on δ -supplement submodules and on δ -small submodules.