lattice; distributive lattice; modular lattice; annihilator; ideal; indexed annihilator
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.
 Davey, B., Nieminen, J.: Annihilators in modular lattices
. Algebra Univ. 22 (1986), 154-158. MR 0870463