Abstract
Let \(n\ge 1\) be an integer. A functor \(F\in \) (mod-R, Ab) is called n-strongly FP -injective if F is isomorphic to some functor \(-\otimes M\) in (mod-R, Ab) with M an \(FP_n\)-injective left R-module. A functor \(G\in \) ((mod-R)\(^{\text{ op }}\), Ab) is said to be n-strongly flat if G is isomorphic to some functor \((-,N)\) in ((mod-R)\(^{\text{ op }}\), Ab) with N an \(FP_n\)-flat right R-module. Precovers and preenvelopes by n-strongly FP-injective and n-strongly flat functors are investigated over a general ring. As applications, special rings are characterized in terms of this two classes of functors.
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Acknowledgements
This research was partially supported by National Natural Science Foundation of China (1197011696), Science and Technology project of Gansu province (20JR5RA517), and College Innovation Fundation of Gansu province (2020A-11). The authors would like to thank the referee for very useful comments and suggestions.
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Communicated by I.B.S.Passi
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Xie, Z., Liu, Z. Some precovers and preenvelopes in functor categories. Indian J Pure Appl Math 52, 903–910 (2021). https://doi.org/10.1007/s13226-021-00094-9
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DOI: https://doi.org/10.1007/s13226-021-00094-9
Keywords
- n-strongly FP-injective functor
- \(FP_n\)-injective
- n-strongly flat functor
- \(FP_n\)-flat modules
- (pre)cover
- (pre)envelope