COMMUNICATIONS IN ALGEBRA, 17(12), 2893-2922 (1989) Shin Ikeda Ngb Vigt Trung Department of Mathematics Institute of Mathematics Box 631, Bd H8 Gifu College of Education 2070 Takakuwa, Yanaizu-cho Hanoi Hashimagan, Gifu Vietnam Japan 1. INTRODUCTION Throughout this paper, let A be a noetherian local ring with maximal ideal m and dimension d 2 1 . Let a be an ideal of A . Then one calls the graded ring the Rees algebra of a . R(a) is an important object of Algebraic Geometry because Proj(R(a)) is the blowing-up of SpecIA) with re- spect to a . Moreover, R(a) is closely related to the associated graded ring whose spectrum is the conormal cone of Spec(A) with respect to a . One of the problems which recently raised some interest is to find neccessary and sufficient conditions for R(a) to be a Cohen-Macaulay ring. This problem originated from the question whether ~(a") is a Cohen-Macaulay ring for all n > 0 if A is a Cohen-Macaulay ring and a is generated by a regular sequence. This question was settled by Barshay [3] and Valla [33]. Their works inspired Goto and Shimoda [lo] 1271 to study local rings with the property that the Rees algebra of every parameter ideal is a Cohen-Macaulay ring. It turned out that they Copyright 0 1989 by Marcel Dekker, Inc. 2894 TRUNG AND IKEDA are a certain kind of Buchsbaum rings, a generalization of Cohen-Macaulay rings 1281. This led to the first partial solution of the above problem...