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 supplementedmodule and 0→N ′ →N →N ′ ′ → 0 an exact sequence, then M isN-lifting if and only if it isN ′-lifting andN ′′-lifting; (2) ifM is a Noetherianmodule, 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) letM 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. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved. 1. Introduction an