A question of Avramov and Foxby concerning injective dimension of complexes is settled in the affirmative for the class of noetherian rings. A key step in the proof is to recast the problem on hand into one about the homotopy category of complexes of injective modules. Analogous results for flat dimension and projective dimension are also established.

We investigate the problem when tensor functor by a bimodule yields singular equivalence. It turns out that this is equivalent to one Hom given same induces triangle equivalence between homotopy categories of acyclic complexes injective modules. give conditions on appears in pair bimodules, defines with level. construct an explicit combinatorial manner, which quadratic monomial algebra and its ...