Abstract
Five open questions on Goldie extending modules were posed by Akalan et al. [Citation1]. The first one and the second one are considered in this article. It is shown that a 𝒢-extending module M with (C 3) is 𝒢+-extending. Moreover, let M = M 1 ⊕ M 2 be a direct sum of 𝒢-extending modules, where M satisfies (C 3) and M 1 is M 2-ojective (or M 2 is M 1-ojective), then M is 𝒢-extending. Other sufficient conditions for a direct sum of 𝒢-extending modules to be 𝒢-extending are obtained.
2000 Mathematics Subject Classification:
ACKNOWLEDGMENTS
The authors thank Gary F. Birkenmeier for valuable suggestions, especially for Example 2.2. The authors wish to thank the referee for very careful reading of the manuscript and also for his/her suggestions.
Notes
Communicated by T. Albu.