Publisher : Department of Mathematics, Kyungpook National University
DOI : 10.5666/KMJ.2009.49.3.557
Title & Authors
On Generalizations of Extending Modules Karabacak, Fatih;
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 and SIP-modules.