Fixed place ideal

Let I be a semi-prime ideal. P 2 Min(I) is called irredundant with respect to I if I , T P ,P2Min(I) P. If I is the intersection of all irredundant ideals with respect to I, it is called a fixed-place ideal. If there are no irredundant ideals with respect to I, it is called an anti fixed-place ideal. We show that each semi-prime ideal has a unique presentation as an intersection of a fixed-place ideal and an anti fixed-place ideal. We also prove that zero ideal of a reduced ring R is anti fixed-place ideal (fixedplace ideal) if and only if Min(R) with Zariski topology has no isolated point (the set of all isolated points of Min(R) with Zariski topology is dense in Min(R)).