Original Article
Kyungpook Mathematical Journal 2009; 49(3): 557-562
Published online September 23, 2009
Copyright © Kyungpook Mathematical Journal.
On Generalizations of Extending Modules
Fatih Karabacak
Anadolu University, Education Faculty, Department of Mathematics, 26470, Eskisehir, Turkey
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.
Keywords: SIP-extending modules, summand intersection property, extending modules