  Let a be an ideal of a commutative Noetherian ring R with identity. We study
finitely generated R-modules M whose a-finiteness and a-cohomological
dimensions are equal. In particular, we examine relative analogues of
quasi-Buchsbaum, Buchsbaum and surjective Buchsbaum modules. We reveal several
interactions between these types of modules that extend some of the existing
results in the classical theory to the relative one.
