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Abstract
ABSTRACTFor any module M, the smallest subcategory of R-modules which is a Grothendieck category and contains M is the category σ[M]. In this article, by introducing two classes of R-modules under the titles -modules and Σn-modules, the notions σ-projective and σ-injective dimension in the category σ[M] have been defined and studied. The relationships between these notions and the corresponding notions defined in the category of R-modules have been investigated. Also, σ-global dimension is defined and some of its properties have been studied.
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