期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2006
卷号：2006
DOI：10.1155/IJMMS/2006/47390
出版社：Hindawi Publishing Corporation
摘要：We introduce the concepts of lifting modules and (quasi-)discrete
modules relative to a given left module. We also introduce the
notion of SSRS-modules. It is shown that (1) if M
is
an 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 only
if M is R-lifting if and only if M is an amply supplemented
SSRS-module; and (3) let M be an amply supplemented SSRS-module
such that Rad(M) is finitely generated, then M=K⊕K′,
where K
is a radical module and K′
is a lifting module.
