$C$-$fp_{n}$-injective and $C$-$fp_{n}$-flat modules

Document Type : Research Paper

Authors

Department of Mathematics, Payame Noor University, Tehran, Iran

Abstract

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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References

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Journal of Mahani Mathematical Research
Volume 14, Issue 1 - Serial Number 31
January 2025
Pages 417-439

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History

  • Receive Date: 21 May 2024
  • Revise Date: 08 November 2024
  • Accept Date: 22 November 2024

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