文摘
Let (A,m) be a Noetherian local ring, let M be a finitely generated Cohen–Macaulay A -module of dimension r≥2 and let I be an ideal of definition for M . Set LI(M)=⨁n≥0M/In+1M. In part one of this paper we showed that LI(M) is a module over R(I), the Rees algebra of I and we gave many applications of LI(M) to study the associated graded module, GI(M). In this paper we give many further applications of our technique; most notable is a complete characterization of good behavior of the Ratliff–Rush filtration modulo a superficial element.