On Generalizations of Extending Modules

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Karabacak F.

KYUNGPOOK MATHEMATICAL JOURNAL, vol.49, no.3, pp.557-562, 2009 (ESCI) identifier identifier

  • 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
  • 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.