The [length] of a finite resolution is the index n such that _________. If M admits a finite projective resolution, the minimal length among all finite projective resolutions of M is called its [projective dimension] and denoted pd(M). 

If M does not admit a finite projective resolution, then by convention the projective dimension is said to be _____.

As an example, consider a module M such that pd(M) = 0. In this situation, the exactness of the sequence 0 → P0 → M → 0 indicates that the arrow in the center is an isomorphism, and hence M itself is_____.