Primary decompositions of three-generated ideals

[摘要] Let I be a 3-generated ideal of height 2 in a RLR (R, tn, k) of dimension d greater than or equal to 3 and J be its unmixed part, i.e. the intersection of all the primary components of I of height 2. In this paper, we will deduce the result of Huneke and Ulrich that if J is Cohen-Macaulay, i.e. pd(R) R/J = 2, then depth R/I greater than or equal to d - 3 from a general and more elementary setting. For the next case that pd(R) R/J = 3, we show that for p is an element of Min(J/I), p(e) not subset of or equal to I:J and p(e) is not contained in any p-primary component of I for e < (h + 1)(h - 3)/2(h - 2) where h = ht p. Also, a negative answer is given to the question of Huneke whether depth R/I greater than or equal to depth R/J - 1 depth R/J greater than or equal to 2.

[发布日期] 1995-12-08