Ding injective envelopes in the category of complexes

2021/07/24 by Gillespie, James, Iacob, Alina
#16E05 #16E10 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.11502

Abstract

A complex X is called Ding injective if there exists an exact sequence of injective complexes … → E₁ → E₀ → E_-1 → … such that X = Ker(E₀ → E_-1), and the sequence remains exact when the functor Hom(A,-) is applied to it, for any FP-injective complex A. We prove that, over any ring R, a complex is Ding injective if and only if it is a complex of Ding injective modules. We use this to show that the class of Ding injective complexes is enveloping over any ring.

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