International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 2, 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
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.