Comptes Rendus
Algebra
Duality pairs, generalized Gorenstein modules, and Ding injective envelopes
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 381-398.

Let R be a general ring. Duality pairs of R-modules were introduced by Holm-Jørgensen. Most examples satisfy further properties making them what we call semi-complete duality pairs in this paper. We attach a relative theory of Gorenstein homological algebra to any given semi-complete duality pair 𝔇=(,𝒜). This generalizes the homological theory of the AC-Gorenstein modules defined by Bravo–Gillespie–Hovey, and we apply this to other semi-complete duality pairs. The main application is that the Ding injective modules are the right side of a complete (perfect) cotorsion pair, over any ring. Completeness of the Gorenstein flat cotorsion pair over any ring arises from the same duality pair.

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DOI: 10.5802/crmath.306
Classification: 16D80, 18G25, 18N40
James Gillespie 1; Alina Iacob 2

1 J.G. Ramapo College of New Jersey School of Theoretical and Applied Science 505 Ramapo Valley Road Mahwah, NJ 07430 U.S.A.
2 A.I. Department of Mathematical Sciences Georgia Southern University Statesboro (GA) 30460-8093 U.S.A.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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James Gillespie; Alina Iacob. Duality pairs, generalized Gorenstein modules, and Ding injective envelopes. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 381-398. doi : 10.5802/crmath.306. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.306/

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