Abstract
This paper is a sequel to [ 111, where we studied the relationships that hold between the arithmetical properties of the Rees ring, 9(I), and the symmetric algebra, Sym(l), of an ideal I (and some of their fibers) and the depth properties of the Koszul homology modules, H,(I; R), on a set of generators of I. The connection between these objects is realized by certain differential graded algebras-the so-called approximation complexes-that are built out of ordinary Koszul complexes. These compIexes show, however. different sensitivities, being acyclic in situations much broader than the usual context of regular sequences. It has been found that certain extensions thereof, d sequences and proper sequences, play here that role of “acyclic sequence.” The interplay between sequences and approximation complexes will be a basic point of view here, where we give:
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