Generalized lifting modules
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2006-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/47390 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |