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On \(D\)-Gorenstein modules. (English) Zbl 0989.13018
Van Oystaeyen, Freddy (ed.) et al., Interactions between ring theory and representations of algebras. Proceedings of the conference, Murcia, Spain. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 210, 159-168 (2000).
Let \(R\) be a local Cohen-Macaulay ring admitting a dualizing module \(D\). The authors introduce and study \(D\)-Gorenstein injective, projective and flat modules. If \(R\) is Gorenstein, then \(D=R\), and \(D\)-Gorenstein injective, projective and flat modules are just the Gorenstein projective, injective and flat modules previously introduced by the authors [see E. E. Enochs and O. M. G. Jenda, Math. Z. 220, No. 4, 611-633 (1995; Zbl 0845.16005), and the authors and B. Torrecillas, J. Nanjing Univ., Math. Biq. 10, No. 1, 1-9 (1993; Zbl 0794.16001)].
For the entire collection see [Zbl 0947.00023].

13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
13C10 Projective and free modules and ideals in commutative rings
13C11 Injective and flat modules and ideals in commutative rings