On Generalizations of Extending Modules

• Journal title : Kyungpook mathematical journal
• Volume 49, Issue 3,  2009, pp.557-562
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2009.49.3.557
Title & Authors
On Generalizations of Extending Modules
Karabacak, Fatih;

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 $\small{C_{11}}$ and SIP-modules.
Keywords
SIP-extending modules;summand intersection property;extending modules;
Language
English
Cited by
1.
CS-Rickart modules, Lobachevskii Journal of Mathematics, 2014, 35, 4, 317
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