Abstract
In a distributive lattice L with 0 set of all ideals of the form (x)* can be made into a lattice A(0)(L), called the lattice of annulets of L. These lattices have been studied by many authors including [4]. Recently, we have extended the concept for n-ideals [1]. We also have studied the set of all n-ideals of the form < x >(*)(n), denoted by A(n)(L) when n is a central element of the lattice. for a fixed element n, a convex sublattice containing n is called an n-ideal. Cornish in [4] has also given the concept of alpha - ideals. In this paper, we have extended that concept around a central element n of a lattice and have introduced the notion of a n ideal. Here, we have given several characterizations of alpha - n - ideals and have included some examples of these n-ideals. We have shown that for a central element n, each prime n-ideal is an alpha - n - ideal if and only if the lattice of principal n -ideals P-n(L) is disjunctive. We have also proved that P-n(L) is sectionally quasi-complemented if and only if each a n ideal is an intersection of minimal prime alpha - n - ideals.