Modules whose finiteness dimensions coincide with their cohomological dimensions

Let a be an ideal of 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 quasi-Buchsbaum, Buchsbaum surjective modules. reveal several interactions between these types modules that extend some the existing results in classical theory to one.