Abstract
Let (A, m) be a regular local ring and I an almost complete intersection ideal (a.c.i. for short) in the sense that p(I) = ht(I) + 1, where #(I) is the least number of generators of I. A quite natural question is : When is A / I a Cohen-Macaulay ring, in particular, if I is a prime ideal. For almost complete intersection prime ideals ~ in a regular local ring A containing a field, the following positive cases are wellknown, s. [5], (5.1): (i) If ht(~3)= 2, then A/~ is Cohen-Macaulay. (ii) If d imA _ _ 2.
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