Homological dimensions of unbounded complexes (Q1175527)

In the classical theory of homological dimensions of modules over associative rings, dimensions are defined in terms of resolutions, and computed in terms of derived functors. This paper explores various notions of projective, injective, and flat dimensions arising from recent constructions of resolutions of unbounded complexes, proposed by N. Spaltenstein and by S. Halperin with the authors of this paper. The different versions of each dimension are compared to each other, and also to the classical concepts, whenever these may be defined. Cohomological characterizations of the dimensions are provided in terms of vanishing of appropriate derived functors. The behavior of the dimensions under change of rings is investigated.