δ -Small Submodules and δ -Supplemented Modules

Yongduo Wang

International Journal of Mathematics and Mathematical Sciences, 2007, vol. 2007, 1-8

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.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:058132

DOI: 10.1155/2007/58132

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