On Generalizations of Extending Modules

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Karabacak F.

KYUNGPOOK MATHEMATICAL JOURNAL, cilt.49, sa.3, ss.557-562, 2009 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 49 Sayı: 3
  • Basım Tarihi: 2009
  • Doi Numarası: 10.5666/kmj.2009.49.3.557
  • Dergi Adı: KYUNGPOOK MATHEMATICAL JOURNAL
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.557-562
  • Anahtar Kelimeler: SIP-extending modules, summand intersection property, extending modules
  • Anadolu Üniversitesi Adresli: Evet

Özet

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.