Two Open Questions On Goldie Extending Modules |
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| Authors: | Dejun Wu Yongduo Wang |
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| Institution: | 1. Department of Mathematics , Northwest Normal University , Lanzhou , Gansu , China wudj2007@gmail.com;3. Department of Applied Mathematics , Lanzhou University of Technology , Lanzhou , Gansu , China |
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| Abstract: | Five open questions on Goldie extending modules were posed by Akalan et al. 1
Akalan , E. ,
Birkenmeier , G. F. ,
Tercan , A. ( 2009 ). Goldie extending modules . Comm. Algebra 37 : 663 – 683 .Taylor &; Francis Online], Web of Science ®] , Google Scholar]]. 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. |
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| Keywords: | Duo module Ejective module Goldie extending module |
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