Abstract
In this paper, we investigate the properties of right orthogonal modules of \({{\mathscr {C}}}\), where \({{\mathscr {C}}}\) is a class of left R-modules. As an application, we investigate the properties of right orthogonal modules of Ding injective left R-modules, and present various characterizations of semisimple and von Neumann regular rings and so on. Moreover, we also consider another cohomology, strong Tate cohomology, which connects the usual cohomology with the Ding cohomology.
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Acknowledgements
Both authors thank the anonymous referees for their very helpful suggestions to improve the paper. The first author was partially supported by NSFC (11571164), the University Postgraduate Research and Innovation Project of Jiangsu Province 2016 (KYZZ16_0034), Nanjing University Innovation and Creative Program for PhD candidate (2016011). The second author was partially supported by NSFC (11371186, 11571341).
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Communicated by Rosihan M. Ali, Dato.
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Zhao, T., Xu, Y. On Right Orthogonal Classes and Cohomology Over Ding–Chen Rings. Bull. Malays. Math. Sci. Soc. 40, 617–634 (2017). https://doi.org/10.1007/s40840-017-0461-4
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DOI: https://doi.org/10.1007/s40840-017-0461-4
Keywords
- \({{\mathscr {C}}}_n\)-injective module
- \({{\mathscr {C}}}_n\)-flat module
- Semisimple ring
- Von Neumann regular ring
- Strong Tate cohomology