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Communications in Algebra Volume 48, 2020 - Issue 12
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Articles

On NCS modules and rings

Fatih KarabacakDepartment of Mathematics, Education Faculty, Anadolu University, Eskisehir, Turkey; View further author information
,
M. Tamer KoşanDepartment of Mathematics, Faculty of Sciences, Gazi University, Ankara, Turkey; View further author information
,
T. Cong QuynhDepartment of Mathematics, The University of Danang - University of Science and Education, Danang City, Vietnam; View further author information
,
D. Duc TaiFaculty of Mathematics, Vinh University, Vinh City, Nghe An Province, Vietnam; View further author information
&
Özgür TaşdemirDepartment of Business Administration, Faculty of Economics and Administrative Sciences, Balkan Campus, Edirne, TurkeyCorrespondence[email protected]
View further author information
Pages 5236-5246 | Received 19 Nov 2019, Accepted 16 Jun 2020, Published online: 03 Jul 2020
 
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Abstract

We give some conditions as to when a (finite) direct sum of NCS modules (if no non-zero complement submodule is small) is again NCS, and also provide various conditions to be sufficient for a submodule of an NCS module to be NCS. Some comparisons between QF-rings, GP-injective rings, AGP-rings and NCS rings are investigated.

2010 Mathematics Subject Classification:

Acknowledgments

The authors would like to express their special thanks to the referee for her/his valuable suggestions.

Additional information

Funding

Dinh Duc Tai was supported by the Funds for Science and Technology Development of the Ministry of Education and Training under the project number B2020-TDV-01.

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