Relative Weak Injective and Weak Flat Modules with Respect to a Semidualizing Module

Elham Tavasoli (), Maryam Salimi () and Siamak Yassemi ()
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Elham Tavasoli: East Tehran Branch, Islamic Azad University
Maryam Salimi: East Tehran Branch, Islamic Azad University
Siamak Yassemi: College of Science, University of Tehran

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 2, 514-520

Abstract: Abstract Let R be a commutative ring, and let C be a semidualizing R-module. We introduce the notion of finitely presented C-injective modules, finitely presented C-flat modules, weak C-injective modules and weak C-flat modules. Some properties of these modules are investigated. It is proved that over weak C-injective ring R, if for a super finitely presented R-module M, $${\text {Hom}}_{R}(M,R)$$ Hom R ( M , R ) is super finitely presented and $${\text {Hom}}_{R}(M,R) \in \mathcal {A}_C(R)$$ Hom R ( M , R ) ∈ A C ( R ) , then the following statements hold: (1) the R-module M is reflexive, (2) the R-module M is Gorenstein projective, provided that $$M\in \mathcal {A}_C(R)$$ M ∈ A C ( R ) .

Keywords: Semidualizing; FP-injective; FP-flat; Weak injective; Weak flat; 13D05; 13D45; 18G20 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00113-9

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