Generalized lifting modules - Yongduo Wang; Nanqing Ding (International Journal of Mathematics and Mathematical Sciences)
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.