International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 47390, 9 pages
doi:10.1155/IJMMS/2006/47390

Generalized lifting modules

Yongduo Wang1 and Nanqing Ding2

1Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, China
2Department of Mathematics, Nanjing University, Nanjing 210093, China

Received 6 March 2006; Accepted 12 March 2006

Copyright © 2006 Yongduo Wang and Nanqing Ding. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.