Global dimension and left derived functors of Hom. (Q2454658)

The right derived functors of the functor Hom along with projective resolutions of (right) modules over a ring \(R\) are the usual tools when studying the right global dimension of \(R\). The authors here give an exposition of the fact this global dimension can also be studied using left derived functors of Hom along with the so-called right projective resolutions of modules. Using these new resolutions you get a new kind of global dimension of \(R\) which is 2 less than the classical global dimension when this dimension is 2 or more. They also consider the case when the classical global dimension is 0 or 1. As applications they give characterizations of right hereditary rings and rings of classical right global dimension at most 2.