Ding Injective Complexes And Their Homological Properties

In this paper, two classes of Ding complexes are introduced, which are called Ding injective and n-strongly Ding injective complexes respectively. Some homo-logical properties and relationships of these classes are investigated. Firstly, some homological characterizations of Ding injective dimension are given. We prove that every complex has a surjective Ding injective precover over QF rings and every com-plex with finite Ding injective dimension admits a special Ding injective preenvelope over any ring. Secondly, we prove that a complex is Ding injective if and only if it is a direct summand of some 1-strongly Ding injective complex. Then we also give a method to construct a 1-strongly Ding injective complex via some n-strongly Ding injective complexes.