$C$-$fp_{n}$-injective and $C$-$fp_{n}$-flat modules
Let $C= {}_SC_R$ be a (faithfully) semidualizing bimodule. This paper begins with the introduction of the concepts of $C$-$fp_n$-injective $R$-modules and $C$-$fp_n$-flat $S$-modules. Subsequently, we investigate various properties associated with classes of modules characterized by $C$-$fp_{n}$-inj...
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Shahid Bahonar University of Kerman
2025-01-01
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| Series: | Journal of Mahani Mathematical Research |
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| Online Access: | https://jmmrc.uk.ac.ir/article_4537_10820a6f30d3de0f3926ab9a3e5a7854.pdf |
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| author | Mostafa Amini Alireza Vahidi Farideh Rezaei |
| author_facet | Mostafa Amini Alireza Vahidi Farideh Rezaei |
| author_sort | Mostafa Amini |
| collection | DOAJ |
| description | Let $C= {}_SC_R$ be a (faithfully) semidualizing bimodule. This paper begins with the introduction of the concepts of $C$-$fp_n$-injective $R$-modules and $C$-$fp_n$-flat $S$-modules. Subsequently, we investigate various properties associated with classes of modules characterized by $C$-$fp_{n}$-injective and $C$-$fp_{n}$-flat dimensions. For instance, we explore Foxby equivalence and the existence of preenvelopes and covers in relation to these classes of modules. Finally, we analyze the exchange properties of these classes and the connections between preenvelopes (or precovers) and Foxby equivalence, particularly within the context of almost excellent extensions of rings. |
| format | Article |
| id | doaj-art-31ceaf9928134af09d318cc0147ffa26 |
| institution | Kabale University |
| issn | 2251-7952 2645-4505 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj-art-31ceaf9928134af09d318cc0147ffa262025-01-04T19:30:18ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052025-01-0114141743910.22103/jmmr.2024.23472.16544537$C$-$fp_{n}$-injective and $C$-$fp_{n}$-flat modulesMostafa Amini0Alireza Vahidi1Farideh Rezaei2Department of Mathematics, Payame Noor University, Tehran, IranDepartment of Mathematics, Payame Noor University, Tehran, IranDepartment of Mathematics, Payame Noor University, Tehran, IranLet $C= {}_SC_R$ be a (faithfully) semidualizing bimodule. This paper begins with the introduction of the concepts of $C$-$fp_n$-injective $R$-modules and $C$-$fp_n$-flat $S$-modules. Subsequently, we investigate various properties associated with classes of modules characterized by $C$-$fp_{n}$-injective and $C$-$fp_{n}$-flat dimensions. For instance, we explore Foxby equivalence and the existence of preenvelopes and covers in relation to these classes of modules. Finally, we analyze the exchange properties of these classes and the connections between preenvelopes (or precovers) and Foxby equivalence, particularly within the context of almost excellent extensions of rings.https://jmmrc.uk.ac.ir/article_4537_10820a6f30d3de0f3926ab9a3e5a7854.pdf$c$-$fp_n$-flat modules$c$-$fp_n$-injective modulesfoxby equivalencesemidualizing bimodules |
| spellingShingle | Mostafa Amini Alireza Vahidi Farideh Rezaei $C$-$fp_{n}$-injective and $C$-$fp_{n}$-flat modules Journal of Mahani Mathematical Research $c$-$fp_n$-flat modules $c$-$fp_n$-injective modules foxby equivalence semidualizing bimodules |
| title | $C$-$fp_{n}$-injective and $C$-$fp_{n}$-flat modules |
| title_full | $C$-$fp_{n}$-injective and $C$-$fp_{n}$-flat modules |
| title_fullStr | $C$-$fp_{n}$-injective and $C$-$fp_{n}$-flat modules |
| title_full_unstemmed | $C$-$fp_{n}$-injective and $C$-$fp_{n}$-flat modules |
| title_short | $C$-$fp_{n}$-injective and $C$-$fp_{n}$-flat modules |
| title_sort | c fp n injective and c fp n flat modules |
| topic | $c$-$fp_n$-flat modules $c$-$fp_n$-injective modules foxby equivalence semidualizing bimodules |
| url | https://jmmrc.uk.ac.ir/article_4537_10820a6f30d3de0f3926ab9a3e5a7854.pdf |
| work_keys_str_mv | AT mostafaamini cfpninjectiveandcfpnflatmodules AT alirezavahidi cfpninjectiveandcfpnflatmodules AT faridehrezaei cfpninjectiveandcfpnflatmodules |