Symmetric bi-T-derivation of lattices

Abstract

In this paper, the notion of a new kind of derivation is introduced for a lattice (L, ?, ?), called symmetric bi-T-derivations on L as a generalization of derivation of lattices and characterized some of its related properties. Some equivalent conditions provided for a lattice L with greatest element 1 by the notion of isotone symmetric bi-T-derivation on L. By using the concept of isotone derivation, we characterized the modular and distributive lattices by the notion of isotone symmetric bi-T-derivation on L.