LAUSR

Let R be a ring and X a chain complex of R -modules. It is proven that if each term $$X_i$$ X i is Ding injective in R -Mod for all $$i\in \mathbb {Z}$$ i ∈ Z , and there exists an integer k such that each $$\mathrm{Z}_iX$$ Z i X is Ding injective in R -Mod for all $$i\ge k$$ i ≥ k , then X is Ding injective in $$\mathrm{Ch}(R)$$ Ch ( R ) . If R is a left coherent ring, then a chain complex X is Ding injective if and only if each term $$X_i$$ X i is Ding injective in R -Mod for all $$i\in \mathbb {Z}$$ i ∈ Z .