Abstract:

Let dwI denote the class of #-injective complexes of left R-modules (i.e., complexes of injective left R-modules). We prove that over left noetherian rings R, the pair (^⊥(dwI), dwI) is a perfect injective cotorsion pair. In particular, we get that every complex of left R-modules has a #-injective envelope. As an application, we prove that over left noetherian rings R, every complex of left R-modules has a special E_tac (I)-preenvelope, where E_tac (I) is the class of complete acyclic complexes of injective left R-modules.

Key words: #-injective complex, cover, envelope, cotorsion pair

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