Closure Operators in Almost Distributive Lattices

The concept of a closure operator ∇ in an ADL R was introduced. If ∇R is the set of all ∇−invariant elements of R, then the concepts of ∇R−ideal, ∇R−prime ideal are introduced. The interrelations between ∇R−prime ideal and minimal prime ideal of R are derived. If B is the Birkhoff centre of R, then a sufficient condition is derived for a B−ideal to be a minimal prime ideal of R.