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

Amini, Mostafa; Vahidi, Alireza; Rezaei, Farideh

doi:10.22103/jmmr.2024.23472.1654

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

Document Type : Research Paper

Authors

Mostafa Amini

Alireza Vahidi

Farideh Rezaei

Department of Mathematics, Payame Noor University, Tehran, Iran

10.22103/jmmr.2024.23472.1654

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.

Keywords

$C$-$fp_n$-flat modules

$C$-$fp_n$-injective modules

Foxby equivalence

semidualizing bimodules

Subjects

Algebra

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