Abstract
We study the concepts of the 𝒫C-projective and the ℐC-injective dimensions of a module in the noncommutative case, weakening the condition of C being semidualizing. We give the relations between these dimensions and the C-relative Gorenstein dimensions (GC-projective and GC-injective dimensions) of the module. Finally, we compare, in some circumstances, the global 𝒫C-projective dimension of a ring and the global dimension of the endomorphisms ring of C.
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