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Gorenstein gr-injective and gr-projective modules. (English) Zbl 0895.16020

The authors study graded Gorenstein rings, proving graded versions for classical results concerning projective and injective dimensions of a module over a Gorenstein ring. Gorenstein gr-injective modules are defined and characterized in terms of complete gr-injective resolutions. A relation between Gorenstein injective objects in the categories \(R\)-mod and \(R\)-gr is presented. In a dual way, similar results are obtained for finitely generated Gorenstein gr-projective modules.

MSC:

16W50 Graded rings and modules (associative rings and algebras)
16D50 Injective modules, self-injective associative rings
16D40 Free, projective, and flat modules and ideals in associative algebras
16E10 Homological dimension in associative algebras
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
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