$C$-$fp_{n}$-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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Shahid Bahonar University of Kerman
2025-01-01
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| Series: | Journal of Mahani Mathematical Research |
| Subjects: | |
| Online Access: | https://jmmrc.uk.ac.ir/article_4537_10820a6f30d3de0f3926ab9a3e5a7854.pdf |
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| Summary: | 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. |
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| ISSN: | 2251-7952 2645-4505 |