Strongly Gorenstein projective, injective, and flat modules
By Najib Mahdou, Driss Bennis. 2006
190 citations recorded by the source corpus.
Abstract In this paper, we study a particular case of Gorenstein projective, injective, and flat modules, which we call, respectively, strongly Gorenstein projective, injective, and flat modules. These last three classes of modules give us a new characterization of the first modules, and confirm that there is an analogy between the notion of “Gorenstein projective, injective, and flat modules” and the notion of the usual “projective, injective, and flat modules”.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/7121ac0ab8bd863d1558b49f99c2d4dac6d36848
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In Algebra and Number Theory
In Geometry and Topology
In Statistical and Nonlinear Physics
Citations in the corpus
- Global Gorenstein dimensions (2006, background): “The principal role of these modules is to characterize the Gorenstein projective and injective modules, as follows � : Lemma 2.6 ([ 1 ], Theorems 2.7).”
- Tate cohomology with respect to semidualizing modules (2009, background): “D. Bennis and N. Mahdou, Strongly Gorenstein projective, injective, and flat modules, J. Pure Appl.”
- Rings Over Which the Class of Gorenstein Flat Modules is Closed Under Extensions (2008, methodology): “Using the definition of Gorenstein flat modules, the equivalence (1) ⇔ (2) is obtained by standard argument.”