Generalization of Auslander-Reiten duality for algebras
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DOI: 10.1080/00927872.2021.1922694
Abstract: Abstract Let R be a Cohen-Macaulay local ring of dimension d with canonical module ωR . In this article we extend Auslander-Reiten duality theorem to certain R-algebras. As a consequence of our argument, we obtain… read more here.
Keywords: generalization auslander; reiten duality; duality algebras; auslander reiten ... See more keywords
Auslander-Reiten duality for Grothendieck abelian categories
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DOI: 10.1090/tran/7379
Abstract: Auslander-Reiten duality for module categories is generalised to Grothendieck abelian categories that have a sufficient supply of finitely presented objects. It is shown that Auslander-Reiten duality amounts to the fact that the functor Ext^1(C,-) into… read more here.
Keywords: duality; grothendieck abelian; abelian categories; auslander reiten ... See more keywords
The generalized Auslander–Reiten duality on an exact category
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DOI: 10.1142/s0219498818502274
Abstract: We introduce a notion of generalized Auslander–Reiten duality on a Hom-finite Krull–Schmidt exact category [Formula: see text]. This duality induces the generalized Auslander–Reiten translation functors [Formula: see text] and [Formula: see text]. They are mutually… read more here.
Keywords: auslander reiten; see text; formula see; generalized auslander ... See more keywords