Abstract :
Let I be a 3-generated ideal of height 2 in a RLR (R, m, k) of dimension d ≥ 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. pdRR/J = 2, then depth R/I ≥ d − 3 from a general and more elementary setting. For the next case that pdRR/J = 3, we show that for p ε Min(J/I), pe n I:J and pe is not contained in any p-primary component of I for e < (h + 1)(h − 3)/2(h − 2) where h = htp. Also, a negative answer is given to the question of Huneke whether depth R/I ≥ depth R/J − 1 if depth R/J ≥ 2.
