GENERALIZED LIFTING MODULES

• Published in: International Journal of Mathematics and Mathematical Sciences Vol. 2006; pp. 1241 - 1249-100
• Main Authors: Wang, Yongduo, Ding, Nanqing
• Format: Journal Article
• Language: English
• Published: Hindawi Limiteds 2006; Hindawi Limited
• ISSN: 0161-1712; 1687-0425
• DOI: 10.1155/IJMMS/2006/47390

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.