Ideals of a distributive lattice with respect to a closure operator

In this paper Quasi-complemented lattices are characterized in terms of dominator ideals. A closure operator is introduced on the ideal lattice and with the help of this operator the concept of closure ideals is introduced and then these ideals are characterized. Further, a one-to-one correspondence between the class of all prime closure ideals of a lattice and the ideal lattice of the lattice of all dominator ideals is established.