Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On Generalizations of Extending Modules

  • Karabacak, Fatih (Anadolu University, Education Faculty, Department of Mathematics)
  • Received : 2008.08.03
  • Accepted : 2008.11.04
  • Published : 2009.09.30
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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.

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