B-sequence and approximations of generalized Cohen-Macaulay ideals

We introduce the notion of b-sequence for finitely generated modules over Noetherian rings, which characterizes long Bourbaki sequences. Our main concern is an application of this notion to generalized Cohen-Macaulay approximation, which we introduced lately. We will show how we can construct long Bourbaki sequences of non-trivial type characterizing generalized Cohen-Macaualy ideals by finding suitable b-sequences.