Gorenstein AC-projective dimension of unbounded complexes

摘要

Recently, the notion of Gorenstein AC-projective (resp., Gorenstein AC-injective) modules was introduced in 3 by which the so-called "Gorenstein AC-homological algebra" was established. Here, we de, ne and study a notion of Gorenstein AC-projective dimension for complexes (not necessarily bounded) over associative rings, which is inspired by Veliche's construction of de, ning Gorenstein projective dimension. In particular, we show that such a dimension can be closely related to the "proper" Gorenstein AC-projective resolutions of complexes induced by a complete and hereditary cotorsion pair in the category of complexes of modules. This enables us to interpret this dimension of a complex in terms of vanishing of the derived functor RHom(R)(-,-). As applications, some characterizations of the Gorenstein AC-projective dimension of a module are also obtained.