On Generalizations of Extending Modules
KYUNGPOOK MATHEMATICAL JOURNAL, vol.49, no.3, pp.557-562, 2009 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 49 Issue: 3
- Publication Date: 2009
- Doi Number: 10.5666/kmj.2009.49.3.557
- Journal Name: KYUNGPOOK MATHEMATICAL JOURNAL
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
- Page Numbers: pp.557-562
- Keywords: SIP-extending modules, summand intersection property, extending modules
- Open Archive Collection: AVESIS Open Access Collection
- Anadolu University Affiliated: Yes
Abstract
A module M is said to be SIP-extending if the intersection of every pair of direct summands is essential in a direct summand of M. SIP-extending modules are a proper generalization of both SIP-modules and extending modules. Every direct summand of an SIP-module is an SIP-module just as a direct summand of an extending module is extending. While it is known that a direct sum of SIP-extending modules is not necessarily SIP-extending, the question about direct summands of an SIP-extending module to be SIP-extending remains open. In this study, we show that a direct summand of an SIP-extending module inherits this property under some conditions. Some related results are included about C-11 and SIP-modules.