Indexed annihilators in lattices
Ivan Chajda · Czech digital mathematics library · 1995
. The concept of annihilator in lattice was introduced by M. Mandelker. Although annihilators have some properties common with ideals, the set of all annihilators in L need not be a lattice. We give the concept of indexed annihilator which generalizes it and we show the basic properties of the lattice of indexed annihilators. Moreover, distributive and modular lattices can be characterized by using of indexed annihilators. M. Mandelker [2] introduced the concept of annihilator in lattice as a natural generalization of the relative pseudocomplement a b of an element a of a lattice L relative to an element b: Definition 1. The annihilator ha; bi for a; b 2 L is the set fx 2 L; a x bg. Evidently, the greatest element of ha; bi, if it exists, is the relative pseudocomplement a b. Although annihilators have some properties in common with ideals, there are also essential distinctions: the set of all annihilators in a lattice L need not be a lattice. This can be seen by means of...