Relative Gorenstein Dimensions |
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Authors: | Driss Bennis J R García Rozas Luis Oyonarte |
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Institution: | 1.Department of Mathematics, Laboratory of Analysis, Algebra and Decision Support, Faculty of Science,Mohammed V University,Rabat,Morocco;2.Departamento de Matemáticas,Universidad de Almería,Almería,Spain |
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Abstract: | In the last years (Gorenstein) homological dimensions relative to a semidualizing module C have been subject of several works as interesting extensions of (Gorenstein) homological dimensions. In this paper, we extend to the noncommutative case the concepts of G C -projective module and dimension, weakening the condition of C being semidualizing as well. We prove that indeed they share the principal properties of the classical ones and relate this new dimension with the classical Gorenstein projective dimension of a module. The dual concepts of G C -injective modules and dimension are also treated. Finally, we show some interesting interactions between the class of G C -projective modules and the Bass class associated to C on one side, and the class of G\({_{C^{\vee}}}\) -injective modules (C ∨ = Hom R (C, E) where E is an injective cogenerator in R-Mod) and the Auslander class associated to C in the other. |
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