The concept of -ideals is introduced in a pseudo-complemented distributive lattice and some properties of these ideals are studied. Stone lattices are characterized in terms of -ideals. A set of equivalent conditions is obtained to characterize a Boolean algebra in terms of -ideals. Finally, some properties of -ideals are studied with respect to homomorphisms and filter congruences.
In this paper, we generalize the notion of supremum and infimum in a poset.
For an algebraic structure or type and a set of open formulas of the first order language we introduce the concept of -closed subsets of . The set of all -closed subsets forms a complete lattice. Algebraic structures , of type are called -isomorphic if . Examples of such -closed subsets are e.g. subalgebras of an algebra, ideals of a ring, ideals of a lattice, convex subsets of an ordered or quasiordered set etc. We study -isomorphic algebraic structures in dependence on the...