Generalized lifting modules

Yongduo Wang and Nanqing Ding

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-9

Abstract:

We introduce the concepts of lifting modules and (quasi-)discretemodules relative to a given left module. We also introduce thenotion of SSRS-modules. It is shown that (1) if M isan amply supplemented module and 0 → N ′ → N → N ″ → 0 an exact sequence, then M is N -lifting if and only if it is N ′ -lifting and N ″ -lifting;(2) if M is a Noetherian module, then M is lifting if and onlyif M is R -lifting if and only if M is an amply supplementedSSRS-module; and (3) let M be an amply supplemented SSRS-modulesuch that Rad ( M ) is finitely generated, then M = K ⊕ K ′ ,where K is a radical module and K ′ is a lifting module.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:047390

DOI: 10.1155/IJMMS/2006/47390

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