نشریه علوم ریاضی و انفورماتیک

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Amini M. Gorenstein (n, d)-Injective and (n, d)-Flat Modules. IJMSI 2026; 21 (2) :61-78
URL: http://ijmsi.ir/article-1-2340-fa.html

Let n, d be non-negative integers. We introduce and study the notions of Gorenstein (n,d)-injective and Gorenstein (n,d)-flat modules by using the notion of special finitely presented, (n,d)-injective and (n,d)-flat modules for any n ≥ d+1. Then we investigate the properties of these modules in case that every special finitely presented module with finite projective dimension (resp. flat dimension) is 2-presented. Moreover, as applications over special coherent rings, we investigate the relationships between Gorenstein (n,d)-injective modules and Gorenstein (n,d)-flat modules, then we obtain that the classes GIⁿ_d (R) and GFⁿ_d (R^op) are covering and preenveloping, where GIⁿ_d (R) and GFⁿ_d (R^op) denote the subcategories of Gorenstein (n,d)-injective left R-module and Gorenstein (n,d)-flat right R-modules, respectively.