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$C$-$fp_{n}$-injective and $C$-$fp_{n}$-flat modules | ||
Journal of Mahani Mathematical Research | ||
دوره 14، شماره 1 - شماره پیاپی 31، فروردین 2025، صفحه 417-439 اصل مقاله (586.06 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22103/jmmr.2024.23472.1654 | ||
نویسندگان | ||
Mostafa Amini* ؛ Alireza Vahidi؛ Farideh Rezaei | ||
Department of Mathematics, Payame Noor University, Tehran, Iran | ||
چکیده | ||
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. | ||
کلیدواژهها | ||
$C$-$fp_n$-flat modules؛ $C$-$fp_n$-injective modules؛ Foxby equivalence؛ semidualizing bimodules | ||
مراجع | ||
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