Note on derivations of lattices (Developments of Language, Logic, Algebraic system and Computer Science)

Abstract

In this paper we consider some properties on derivations of lattices and show that (i) for a derivation d of a lattice L with the maximum element 1, it is monotone if and only if d(x) leq d(1) for all x in L (ii) a monotone derivation d is characterized by d(x)=xwedge d(1) and (iii) simple characterization theorems of modular lattices and of distributive lattices are given by derivations.